Entanglement-assisted quantum networks principles, techniques, developments and challenges

On July 11th, the review paper "Entanglement-Assisted Quantum Networks: Mechanics, Enabling Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions" was published online in IEEE Communications Surveys and Tutorials, a well-known journal in the field of communications.

 

 

This work is the first to construct a knowledge map of entanglement-assisted quantum networks, which provides a profound and comprehensive description of the cutting-edge research field of entanglement-assisted quantum networks from the perspectives of fundamental principles of quantum mechanics, entanglement-enabled quantum technologies, network components, network design, and quantum applications, specifically analyzes the key technological challenges in this field, and clearly points out the future research directions for the design of the network in this field, which will be important for the future of quantum networks. It also clearly points out the future research direction of this field in terms of network design, which is of great significance and far-reaching impact on the construction and development of the future quantum Internet.

 

This research was supported by the Guiding Project of Quantum Communication and Quantum Computer Major Program of Anhui Province (AHY150300), the Science and Technology Innovation 2030 Major Program of the Ministry of Science and Technology (2021ZD0301301), and the Outstanding Membership Support Program of the Chinese Academy of Sciences' Young Innovators Association (Y202093).

 

In this section, the experimental team reviews a number of enabling technologies that support the interconnection of quantum nodes in entanglement-assisted quantum networks: from point-to-point entanglement distribution to quantum bit transmission, such as quantum dense coding, quantum invisible state transfer, entanglement purification, quantum error correction, entanglement switching, and quantum memory. In addition, the functions of these enabling technologies are discussed, and the development status of these enabling technologies is presented to demonstrate that the establishment of entanglement-assisted quantum networks is not far off.

 

1) Preparation and distribution of entanglement

 

Entanglement plays a crucial role in quantum information transmission because the communicating parties need to share entangled quantum bit pairs. Therefore, a quantum technology that enables entanglement of quantum nodes is needed as the cornerstone of entanglement-assisted quantum networks. In general, the establishment of entanglement between neighboring quantum nodes is achieved through two key operations: entanglement preparation and entanglement distribution. Among them, entanglement preparation aims to generate entangled quantum bits, while entanglement distribution enables prepared entangled quantum bits to be shared by spatially separated quantum nodes with the help of quantum channels. Here, the team describes three typical schemes that can establish entanglement between neighboring quantum nodes by preparing and distributing entangled quantum bits:

 

- Parametric downconversion schemes. The first scheme is realized with the help of a spontaneous parametric downconversion (SPDC) process based on a nonlinear crystal. Due to the availability of efficient polarization control elements and the relative insensitivity of most materials to birefringent thermally induced drifts, polarized photons are commonly used in experiments to generate entangled quantum bits. In experiments, this scheme is well established for demonstrating tests of quantum dense coding, stealthy state transfer, and Bell's inequality. Currently, SPDC processes based on nonlinear optical materials are still a hot research topic in the field of entanglement preparation. The future development direction of SPDC-based entanglement light sources is to reduce the loss, improve the purity and degree of entanglement, and combine with micro- and nanophotonic devices to improve the scalability and practicality of entanglement light sources.

 

 

Entanglement distribution between Alice and Bob based on parametric downconversion.

 

- Single-atom excitation scheme. Another scheme for preparing and distributing entangled quantum bits between two spatially separated quantum nodes is realized based on single-atom excitation. This scheme utilizes atoms tightly coupled to an optical cavity to establish entanglement between two quantum nodes directly connected by a photonic channel. Specifically, the quantum node Alice transfers the internal state of the atom to an optical state in the cavity mode by means of a laser beam. In other words, the atom is first excited by the laser beam at Alice, and the emitted photons become entangled with the internal state of the atom. Then, the atom-entangled photons are released from Alice's cavity and move along the photon channel into another cavity of the quantum node Bob. In Bob's cavity, the photon is coherently absorbed and its polarization is mapped onto the internal state of the atom. As a result, the two atoms located at Alice and Bob become remotely entangled.

 

 

Entanglement distribution between Alice and Bob based on single-atom excitation.

 

- Dual-atom excitation scheme. The third entanglement distribution scheme is realized based on the simultaneous excitation of two atoms. First, two laser beams at Alice and Bob excite two atoms at the same time, which causes each localized cavity to emit a photon entangled with the corresponding atom. Then, the two photons entangled with the atoms leave the local cavities and propagate as a wave packet along the quantum channel to the beam splitter, where a BSM operation is performed to realize the entanglement exchange. Upon completion of the BSM operation, the atom located at Alice establishes entanglement with Bob's atom, i.e., a pair of entangled atoms is assigned to Alice and Bob.Compared with the single-atom excitation scheme, the dual-atom excitation scheme can effectively extend the distance of entanglement distribution with the assistance of a third party. However, the realization of the dual-atom excitation scheme requires two quantum nodes to be symmetrically connected to a third party that is responsible for performing the BSM operation and distributing the entangled quantum bits at the same time, which greatly hampers the application of this scheme in entanglement-assisted quantum networks.

 

 

Entanglement distribution between Alice and Bob based on simultaneous excitation of two atoms.

 

2) Quantum dense coding

 

In classical information theory, the upper limit of the amount of classical information that can be transmitted by a channel is called the channel capacity. However, with the help of quantum entanglement and superposition principles, the amount of classical information transmitted through a quantum channel will far exceed this upper limit. In order to realize the increase in channel capacity, Bennett first theoretically proposed a quantum dense coding scheme in 1992, which emerged to break the Holevo boundary - i.e., a quantum bit can carry the classical information of at most one classical bit. Bennett's scheme shows that two classical bits can be transmitted from Alice to Bob, who is entangled with Alice, by transmitting just one quantum bit.This gives the entanglement-assisted classical information transmission method twice the channel capacity. Formally, quantum dense coding is a quantum communication technique that utilizes the entanglement property to transmit classical bits.

 

 

The process of realizing quantum dense coding using a Bell state entanglement system is shown in Fig. Alice and Bob first share a pair of entangled quantum bits (i.e., Bell states) distributed by an EPR source through a quantum channel. Alice then encodes two classical bits (00, 01, 10, or 11) by performing the corresponding quantum operation on her locally owned entangled quantum bits and sends this entangled quantum bits to Bob over the quantum channel.Upon receipt of the encoded entangled quantum bits, Bob performs a local BSM operation on the two entangled quantum bits to decode the transmitted classical bits. In this way, Bob can obtain the two classical bits that Alice wants to send based on the final state of the entangled system that he has.

 

 

Quantum dense coding circuits

 

Unlike the QKD technique, which can only distribute random keys used to secure classical communication, quantum dense coding can utilize entangled quantum bit pairs to directly transmit specific binary bit strings between the two communicating parties, further improving the security of classical communication.

 

3) Quantum invisible state transmission

 

In 1993, Bennett et al. first proposed the concept of quantum invisible transmission, and were the first to explore the use of classical communication and entangled quantum bits to transmit unknown quantum bits from one node to another node directly over long distances, and carried out an experimental demonstration in 1997. Formally, quantum stealth teleportation is a quantum technique that utilizes the properties of classical communication and quantum entanglement to transmit quantum information between two communicating parties, even if they are not connected via a quantum channel. In other words, Bob, who shares the Bell state with Alice, can perfectly "copy" the unknown quantum bits that Alice wants to transmit locally based on the classical information that Alice sends, thus realizing the transmission of quantum information between the two communicating parties without being affected by the noise of the quantum channel.

 

QKD and Quantum Dense Coding can only utilize quantum mechanical properties to transmit classical information (random keys and specific binary bits). In other words, QKD and quantum dense coding are often used as an adjunct to protect the classical communication between Alice and Bob.QKD is easy to implement in the current state of the art and is the first quantum secure communication technology to be deployed and used to provide secure services. Unlike QKD, which is designed to distribute random keys between the communicating parties, quantum dense coding enables the transmission of specific classical binary bits. However, its practical application is limited by the development of physical devices. Similar to quantum dense coding, stealthy transmissions also require the sharing of entangled quantum bits between the communicating parties. However, quantum invisible transfer is fundamentally different from quantum dense coding because it realizes the transmission of quantum information rather than classical information. In addition, during quantum stealthy state transfer, the state of the quantum bits being stealthily transferred is not affected by the post-measurement collapse. Therefore, compared with QKD and quantum dense coding, quantum invisible state transfer plays a more crucial role in entanglement-assisted quantum networks.

 

In order to realize the "copying" of a quantum bit, all the information of the unknown quantum bit has to be divided into classical and quantum information and sent to Bob through the classical channel and the quantum channel, respectively; it is worth noting that the quantum information of the unknown quantum bit will not be transmitted to Bob through the real physical channel. Due to the non-local nature of the Bell state, the quantum information of the unknown quantum bit can be "transferred" to Bob's entangled quantum bit instantaneously after the BSM operation. Therefore, the realization of the quantum invisible state transfer only requires the classical information to be transmitted through the classical channel after the entangled state is shared between the two communicating parties, i.e., the transmission of the unknown quantum bit is not interfered by the quantum channel noise.

 

 

Standard quantum invisible state transfer system. After entanglement distribution, Alice and Bob share the Bell state, i.e., each has an entangled quantum bit locally. Then, Alice performs a BSM operation on the unknown quantum bit she wants to send to Bob along with the local entangled quantum bit, and sends the measurement results (two classical bits 00, 01, 10, or 11) to Bob over the classical channel.Finally, based on the measurement results, Bob performs the corresponding You operation on his own entangled quantum bit to get the invisibly transmitted quantum bit being the Finally, according to the measurement result, Bob performs the corresponding you operation on his own entangled quantum bit to get a "copy" of the invisibly transmitted quantum bit - i.e., the state information of the invisibly transmitted quantum bit is mapped onto Bob's local entangled quantum bit. Thus, with the help of quantum stealth state transfer technology, unknown quantum bits can be transferred from Alice to Bob, no matter how far apart they are.

 

Most notably, although quantum stealth transmutation can transmit quantum information without a real physical channel, the unknown quantum bits will not propagate faster than the speed of light because quantum stealth transmutation cannot be separated from classical communication. In addition, although the quantum bits being stealthily transmitted will not be directly affected by channel noise, channel noise will lead to a low-fidelity entangled system shared by the two communicating parties, thus affecting the success probability of quantum stealthy transmission. Therefore, high-fidelity entanglement distribution between quantum nodes is needed to effectively realize quantum bit transformation.

 

4) Entanglement purification

 

Entanglement purification was originally proposed in the context of quantum communication to solve the problem of long-distance communication over noisy quantum channels. Since quantum bits are extremely fragile, noise in the quantum channel as well as interactions with uncontrolled environments, including quantum memories and measurement devices, can lead to the expected entangled quantum bits being generated only with a certain non-unit fidelity. As a result, a purely entangled system will decay into a hybrid entangled system after distribution over a noisy quantum channel, leading to various errors in quantum information processing. Notably, high-fidelity entangled systems shared by distant quantum nodes are crucial for realizing high-performance and reliable quantum applications. For example, the fidelity directly affects the measurement accuracy in quantum sensing. Higher fidelity can provide more precise measurements, thus improving the reliability and accuracy of applications. Entangled systems with low fidelity can lead to increased inaccuracy or unpredictability in quantum sensing. Therefore, a design that protects quantum information is needed in entanglement-assisted quantum networks. The most well-known approach is entanglement purification - i.e., protecting quantum information by improving the quality of the entangled system.

 

Entanglement purification is the process of extracting maximally entangled states from some partially entangled states using localized measurements and classical communication (LOCC). In other words, entanglement purification is a powerful tool to extract high-fidelity entanglement from a collection of low-quality entanglement, which plays a crucial role in long-distance quantum information transmission. In short, entanglement purification can improve the fidelity of entangled systems at the cost of reducing the number of entangled quantum bit pairs.

 

 

As shown in the figure, before entanglement purification, there are M copies of non-maximally entangled states with fidelity F1. During entanglement purification, these entangled quantum bit pairs are processed to produce fewer and less noisy copies. Therefore, after entanglement purification, N pairs of entangled quantum bit pairs with fidelity F2 are generated from the original M non-maximally entangled quantum bit pairs, i.e., N < M and F1 < F2.

 

Entanglement-assisted quantum networks require efficient and low-overhead entanglement purification schemes for high-quality entanglement distribution. On the one hand, successful distribution of entangled quantum bit pairs between neighboring quantum nodes is challenging due to the inherent loss and noise of quantum channels. The success probability of point-to-point entanglement distribution is usually negatively exponential with the physical length of the quantum channel. Therefore, entangled quantum bit pairs shared by neighboring quantum nodes are a scarce network resource. The entanglement purification scheme needs to be as efficient as possible to improve the utilization of entanglement resources. On the other hand, the fidelity of an entangled state shared by two distant quantum end nodes is approximately equal to the product of the fidelity of the entangled states measured on the selected path.

 

In order to produce high quality end-to-end entanglement, the entanglement usually needs to be purified to have high fidelity. As a result, multiple rounds of purification operations need to be performed between neighboring quantum nodes, thus consuming more entanglement resources. Low overhead entanglement purification schemes help to improve the performance of entanglement-assisted quantum networks.

 

5) Quantum Error Correction

 

Quantum communication is the most complex application of quantum information processing. However, the transmission of quantum bits over noisy physical channels inevitably leads to errors in quantum information, which greatly hampers the commercial application of quantum communication. Therefore, how to fully preserve the quantum properties of quantum information while transmitting it is a crucial issue. Referring to classical communication, quantum communication requires quantum error correction (QEC) designs that can protect quantum information during transmission or recover it after transmission. In this context, QEC codes are introduced as an effective error correction method that utilizes specific coding to protect quantum information.

 

Although the idea of designing QEC codes is similar to that of classical error correction codes: i.e., introducing redundant information in a suitable way to improve the information's immunity to interference, it is not a simple extension of classical error correction codes due to the uniqueness of quantum mechanics. There are three major challenges in designing QEC codes:

 

- No Cloning Theorem: for classical error correcting codes, redundant information is introduced by preparing multiple copies of a single bit; however, quantum bits strictly follow the no cloning theorem. Therefore, copying quantum bits to introduce redundant quantum information is not possible.

 

- Errors are continuous: in classical communication, the state of a single bit is deterministic; therefore, only bit-flip errors need to be considered for errors in classical information. However, due to the superposition principle, the degree of error in quantum information is greater than that of classical information. Quantum bits are susceptible to both bit flips and phase flips. Therefore, the QEC code must have the ability to detect both types of errors.

 

- Post-measurement crash: in classical systems, arbitrary properties of bit registers can be measured without risking compromising the encoded information for erroneous patterns. However, any measurement operation in the quantum world corrupts the state of a quantum bit, making it unrecoverable.

 

These problems make designing quantum error correction codes quite challenging compared to classical error correction codes.

 

Fortunately, none of the above problems are fatal to QEC code design. We can adopt some clever methods to overcome these difficulties. First, in order to break the limitations of the no-cloning theorem, a single quantum bit can be encoded as a complex entangled state. In this way, we can introduce redundant information into the QEC encoding without violating the basic principles of quantum mechanics. Second, although the variety of quantum errors is a continuum, it is a linear combination of the three fundamental quantum errors (corresponding to the three bubbleley matrices). Therefore, all quantum errors can be corrected once these three fundamental quantum errors are corrected. Finally, the quantum error pattern can be obtained by a special kind of projection measurement called "stabilizer measurement": i.e., only some extra quantum bits are measured, not all of them. In this way, quantum coherence is preserved and the results of the measurement operation can fully reflect the quantum error pattern.

 

In short, these novel ideas have paved the way for the design of QEC codes to correct quantum errors, thus accelerating the development of quantum information technology.

 

6) Entanglement Swapping

 

Establishing entanglement between distant quantum nodes is one of the important cornerstones for realizing distributed quantum applications. However, the likelihood of success of direct distribution of entanglement between two quantum nodes decreases exponentially with the physical distance of the quantum channel, i.e., it is extremely difficult for two distant quantum nodes to share entangled quantum bit pairs. Therefore, in entanglement-assisted quantum networks, there is a need for an end-to-end quantum technology that can extend the entanglement distribution distance from short point-to-point to long distances. However, quantum information technology strictly follows the no-cloning theorem. Therefore, the signal amplification and regeneration methods employed in classical communication do not work in long-distance quantum communication. Inspired by the quantum invisible transmission state, where entangled quantum bits separated from entangled quantum bit pairs can be transmitted from one quantum node to another to establish entanglement between two distant quantum nodes, entanglement swapping has been proposed as an effective solution for generating long-distance entanglement between distant quantum nodes.

 

 

Principle of Entanglement Swapping.

 

Entanglement swapping is essentially a LOCC operation for effectively extending the distance of entanglement distribution. It is worth noting that entanglement swapping brings some network problems during remote entanglement distribution. First, due to the imperfections of physical devices, entanglement switching presents probabilistic characteristics. Therefore, in entanglement-assisted quantum networks, it is crucial to choose a path with a high probability of success for remote entanglement distribution. In addition, unlike the classical network where packets are forwarded from the source node to the destination node, the switching operation can be executed in parallel on the selected path to improve the entanglement distribution rate. However, considering the probabilistic nature of entanglement switching, entanglement needs to be tracked during remote entanglement distribution. Due to the postmeasurement collapse phenomenon, there is also a need to avoid competition for entanglement resources by the exchange operation. Therefore, entanglement-assisted quantum networks need to manage the parallel execution of exchange operations.

 

7) Quantum Memory

 

Quantum memories are important in many ways, including single-photon sources, quantum repeaters, vulnerability-free Bell inequality tests, communication complexity protocols, and implementations of precision measurements. Quantum memories are important for several reasons. First, as the smallest unit of microscopic particles, quantum states are susceptible to noisy environments. Another reason is that quantum manipulation during both entanglement preparation and remote entanglement distribution has a probabilistic character. Therefore, quantum memory is necessary to store and synchronize randomly generated entangled quantum bits in entanglement-assisted quantum networks.

 

 

The above table provides a comprehensive comparison of the three types of quantum memories in terms of four key metrics, namely, fidelity, efficiency, lifetime, and room temperature utility.

 

Solid-state quantum memories excel in fidelity and lifetime due to the fact that solid-state materials, especially those doped with rare-earth ions, have long optical coherence times and wide optical absorption bandwidths. Solid-state quantum memories can achieve fidelity of 0.999 and lifetimes on the order of seconds. However, currently realized solid-state quantum memories have low efficiency (only 56%) and poor performance at room temperature. Atom cluster quantum memories perform well in terms of efficiency because photons are not easily absorbed by atoms. However, atomic sequence quantum memories perform poorly in terms of fidelity and lifetime because the atoms move very violently and collisions between them generate high noise. Optical quantum memories have good utility at room temperature but perform poorly in terms of fidelity, efficiency and lifetime due to photon losses and channel noise. In conclusion, each type of quantum memory has its advantages and disadvantages, and how to utilize their advantages in practical application scenarios remains to be explored.

 

In the past decades, quantum memories have evolved from initial theoretical demonstrations to near practicality today, providing advantages for quantum information technology. In the latest research, quantum memories have a storage fidelity of up to 99% under laboratory conditions. In addition, the latest quantum memories can store a photon for more than an hour. Similar to classical memories, quantum memories can be regarded as a combination of multiple independent storage units with high fidelity, high efficiency and long storage time. Quantum memories capable of providing flexible storage services are expected to be realized in the near future, thus facilitating the development of quantum repeaters to further support entanglement-assisted quantum networks.

 

In terms of physical structure, the entanglement-assisted quantum network can be regarded as a mesh structure consisting of three kinds of network elements: physical channels, network devices and quantum terminal nodes. First, physical channels are used to transmit microscopic particles between neighboring quantum nodes; second, network devices (such as quantum repeaters and quantum routers) are the key to constructing large-scale, wide-area entanglement-assisted quantum networks. Quantum repeaters utilize the unique properties of entanglement to overcome the distance limitation caused by the inherent loss of physical channels, thus expanding the communication range. Quantum routers aim to aggregate numerous quantum nodes to expand the network scale. Quantum end nodes support the top quantum applications running on them by transmitting and processing quantum information.

 

 

Abstract structure of large-scale wide-area entanglement-assisted quantum network

 

Specifically, a small number of quantum terminal nodes converge into a small-scale localized quantum network aided by network devices and physical channels, and the network devices are interconnected through physical channels to form a wide-area core quantum network with a mesh topology, i.e., a cloud icon. In this way, the core quantum network can connect many local area quantum networks to form a large-scale, wide-area entanglement-assisted quantum network. Any pair of neighboring quantum nodes can establish entanglement links by sharing pairs of entangled quantum bits, which is an important resource for quantum information transmission. With the help of quantum routers and quantum repeaters, any pair of quantum terminal nodes can "couple" multiple entangled links along selected paths to establish long-distance entanglement connections, thus realizing long-range quantum information transmission.

 

 

The above figure illustrates the meaning of entanglement-assisted quantum networks from the aspects of quantum mechanics, enabling technology, network elements, network design and various quantum applications.

 

First, entanglement-assisted quantum networks follow the fundamental laws of quantum mechanics, such as the unclonability theorem, superposition states, uncertainty principle and quantum entanglement. These unique properties, which have no counterparts in classical mechanics, give quantum information technology a huge advantage over classical information technology. The preparation, storage, transmission and processing of quantum information are governed by the unique properties of quantum mechanics. Therefore, entanglement-assisted quantum networks are fundamentally different from classical networks.

 

Second, enabling technology is an important part of entanglement-assisted quantum networks. Unlike classical networks, the interconnection between long-distance quantum nodes is realized based on entanglement. Therefore, entanglement preparation, entanglement purification, and entanglement switching play a key role in establishing high-fidelity entanglement between long-distance quantum nodes, and these enabling technologies are able to support quantum stealthy state transfer, thus realizing quantum information transmission.

 

Third, physical network elements, including physical channels, quantum terminal nodes, and network devices, are the necessary physical equipment for realizing large-scale, wide-area entanglement-assisted quantum networks. It is worth noting that quantum operations including entanglement distribution, entanglement switching and quantum invisible state transfer are realized with the help of classical communication. Therefore, the physical channel involves both quantum and classical channels. In entanglement-assisted quantum networks, quantum terminal nodes and network devices are connected through physical channels according to specific rules to form a mesh topology, thus constructing the underlying infrastructure. This infrastructure is an ideal platform to realize remote entanglement distribution among quantum terminal nodes, thus supporting various quantum applications. Although entanglement-assisted quantum networks are fundamentally different from classical networks, they share similarities in the categories and functions of network elements. Therefore, the structural design principles of classical networks can provide guidance for the realization of future entanglement-assisted quantum networks.

 

Fourth, network design is crucial for realizing effective and efficient remote entanglement distribution in entanglement-assisted quantum networks. Notably, entanglement-assisted quantum networks are more than a simple collection of multiple independent paths used to establish end-to-end entanglement connections. It is necessary to manage concurrent network tasks in order to meet application requirements in an orderly and efficient manner. Moreover, the management solutions used in classical networks cannot be directly applied to entanglement-assisted quantum networks. Therefore, network designs such as routing algorithms, scheduling schemes and resource allocation algorithms need to be investigated as administrators to manage concurrent tasks and ensure the quality of service in entanglement-assisted quantum networks.

 

Finally, quantum applications running on quantum terminal nodes, including quantum communication, quantum computing, quantum sensing, and quantum cryptography, can fully exploit the potential of quantum information technology. Quantum communication is one of the most interesting applications in applied quantum physics and is closely related to quantum invisible transmission. It is based on quantum properties and realizes the unconditional secure transmission of quantum information between the two communicating parties. Quantum computing is a perfect combination of quantum physics, computer science and information theory. Due to the existence of superposition states, quantum computing can be exponentially faster compared to classical computing. Therefore, quantum computing has a broad application prospect in the era of big data. Quantum sensing is one of the most advanced quantum applications. It utilizes quantum resources to improve the sensitivity or precision of measurements based on quantum properties, surpassing the possibility of classical measurements. As a result, quantum sensing can significantly enhance the performance of many practical tasks, including gravitational wave detection, astronomical observation, microscopy, target detection, data reading, atomic clocks, and biological detection. Quantum cryptography is a science that utilizes quantum properties to perform cryptographic tasks. The best known and most developed application of quantum cryptography is QKD, which provides an information-theoretically secure solution to the problem of key exchange in classical networks. Quantum cryptography also corresponds to a range of other ideas broadly related to bit commitment, such as quantum secret sharing.

 

Overall, quantum applications offer significant advantages over classical applications based on the unique features of quantum mechanics. Notably, many quantum applications require quantum end nodes to establish entanglement. Therefore, remote entanglement distribution between quantum terminal nodes is one of the components of entanglement-assisted quantum networks.

 

In summary, entanglement-assisted quantum networks can be defined as a promising platform consisting of quantum nodes and physical channels that follow the fundamental laws of quantum mechanics. These networks are intended to support breakthrough quantum applications; they enable remote entanglement distribution and quantum information transfer between quantum end nodes under the control of the network design.

 

2) Development stage

 

Similar to the development trajectory of classical information formation technologies, quantum information technologies will evolve from point-to-point quantum communications to large-scale entanglement-assisted quantum networks supporting various quantum applications. The functions that can be realized by entanglement-assisted quantum networks are driven by the development of quantum physical devices, and thus this development trajectory shows the great diversity of functions at different stages. Thus, the development of entanglement-assisted quantum networks is not only reflected in the size of the network, but also in its functionality.

 

 

Development stages of entanglement-assisted quantum networks

 

- Quantum Key Distribution Network (QKDN)

 

A quantum key distribution network (QKDN) is a quantum network that distributes random secret keys among QKD nodes according to the fundamental laws of quantum mechanics. This phase is quite different from the others in that it focuses on theoretically realizing unconditionally secure key distribution to enhance the security of classical communication rather than quantum information transmission. Optical devices and QKD protocols drive the development of QKDN: the maturity of optical devices has pushed the QKD technology from the laboratory to practical applications; at present, some small-scale QKDNs are available for commercial services, and satellite-to-ground QKDNs have also been verified in experiments.

 

It is worth noting that the inherent loss and noise of quantum channels greatly limit the rate of key distribution between neighboring QKD nodes. For example, the first QKD metropolitan network, DARPA, can only provide key distribution service with a maximum key rate of 10kbps. In order to effectively realize long-distance key distribution, these QKD networks mainly use trusted repeaters to overcome the distance limitation. Trusted repeaters are a class of quantum devices that contain multiple pairs of quantum transmitters and receivers, and work by utilizing classical cryptographic operations (e.g., XOR operations) to transmit quantum keys. However, in real-world QKDNs, it is challenging to guarantee that all trusted repeaters are fully trusted. Therefore, remote key distribution based on trusted repeaters faces severe security challenges.

 

Fortunately, some innovative QKD protocols, such as Measurement Device Independent QKD (MDI-QKD) and Two-Field QKD (TF-QKD), have been proposed to overcome the distance limitation by introducing untrusted third parties to improve the remote key distribution rate. However, large-scale QKDN requires the integration of trusted repeaters and untrusted third parties, which reduces the security level of QKDN. One way to extend the key distribution distance and achieve a high level of security is to use quantum repeaters. Quantum repeaters establish long-distance entanglement by performing entanglement exchange. With the help of a quantum repeater, two distant QKD nodes can share entangled quantum bit pairs and achieve unconditionally secure key distribution using the entanglement-based QKD protocol. However, idealized quantum repeaters are still not available.

 

Therefore, the establishment of large-scale and wide-area QKDNs to distribute keys to support classically secure communication will remain a focus of quantum networking research.

 

- Preparation and Measurement Networks (PMN)

 

This phase attempts to provide end-to-end quantum functionality due to the rapid development of quantum devices such as light sources and detectors. In other words, encrypted information can be transmitted in the form of coded quantum bits using specific coding rules. Thus, PMNs enable end-to-end information transmission by preparing and measuring quantum bits, which is different from the hop-by-hop transmission of quantum keys with the help of trusted repeaters in QKDN.

 

At this stage, any quantum node encodes quantum bits and transmits them to the next quantum node through a quantum channel; then, that node measures the received quantum bits and prepares the quantum bits to be sent to the next node based on the measurement. In the process of information transmission between quantum terminal nodes, each quantum node in the communication path is both an encoder and a decoder. The classical information transfer based on the "preparation-measurement" method, also known as quantum-safe direct communication (QSDC), consists of two realizations: one based on single photons and the other on entanglement.

 

Nowadays, photon loss and quantum decoherence are still the main obstacles for PMN. Maintaining the accuracy of classical information in long-distance communication is a challenge. In addition, since the key to QSDC between neighboring quantum nodes lies in block (i.e., quantum bit sequence) transmission, PMNs are very dependent on quantum memory. It is important to note that the preparation and measurement functions are not equivalent to transmitting arbitrary quantum information, since the transmitted quantum bits are not unknown, i.e., the essence is still transmitting classical information.

 

- Entanglement Distribution Network (EDN)

 

EDN enables end-to-end entanglement distribution in a microscopic or heralded manner. The development of entanglement distribution technology has facilitated the implementation of EDN. In this stage, end-to-end entanglement is established by repeatedly performing entanglement exchanges along a relay chain consisting of multiple quantum repeaters. As mentioned above, the realization of end-to-end secure communication in QKDN and PMN relies heavily on intermediate quantum devices. In QKDN, trusted repeaters are required to perform classical cryptographic operations to extend the key distribution distance. The premise that each trusted repeater will not maliciously disclose the quantum key ensures the security of end-to-end key distribution.

 

In PMN, the premise of realizing end-to-end secure communication is that each quantum node is secure, i.e., the encrypted information will not be maliciously leaked by the quantum nodes. The main advancement of EDN compared to the previous stages is that device-independent application protocols can be realized. More specifically, each quantum node in EDN is untrustworthy, while each intermediate node between a pair of quantum end nodes is transparent to the end-to-end application protocol, i.e., information leakage from the intermediate nodes will not affect the realization of the end-to-end application. Device-independent application protocols are realized based on entanglement properties. This phase does not strongly require quantum nodes to be configured with quantum memory. To minimize the negative impact of quantum decoherence, entanglement distribution is usually triggered on demand. Therefore, in addition to the development of physical devices responsible for entanglement preparation, the entanglement distribution scheduling design is crucial for the performance of EDNs. Notably, multi-party entanglement generation cannot be realized at this stage.

 

- Quantum Memory Networks (QMNs)

 

The realization of quantum memory networks benefits from the fact that quantum memories can operate like classical memories in a room temperature environment. This phase requires a local quantum memory for each quantum node in the network.

 

Unlike in EDNs where entangled quantum bits are prepared on demand, in QMNs entangled quantum bits can be stored in the quantum memory for a certain period of time, which helps to mitigate the probabilistic character of quantum operations such as entanglement distribution and entanglement swapping. Thus, by exploiting the capability of localized quantum memory, QMNs can enable complex quantum applications such as blind quantum computing . This stage is a turning point in the development of the network. In other words, a quantum network can transfer quantum information deterministically between any pair of quantum terminal nodes, thus realizing some less complex distributed quantum tasks.

 

In addition, the size of quantum memory is crucial for QMNs. Therefore, the development of large size, high fidelity, high lifetime, efficient and room temperature applicable quantum memories is crucial for realizing QMNs.

 

- Fault-tolerant quantum networks (FQNs)

 

FQNs support a number of quantum applications by distributing entangled quantum bits. FQNs are characterized by the ability to perform local quantum operations in a fault-tolerant manner. Fault tolerance implies that all errors caused by noisy quantum channels, measurement devices, and quantum memories are negligible by increasing network resources. Therefore, FQNs strongly require high performance quantum memories to store more network resources. In addition, QEC techniques play a pivotal role in FQNs.

 

At this stage, the available fault-tolerant local operations allow the execution of local quantum computations with higher accuracy and protocols with arbitrary number of communication rounds. In short, we can consume more network resources to mitigate quantum decoherence and thus support high-quality quantum bit operations. Thus, in addition to QMNs that enable deterministic transmission of quantum information, many quantum applications, such as clock synchronization and distributed quantum computation, can be implemented in FQNs.

 

- Quantum Information Networks (QINs)

 

This phase is the final stage in the development of entanglement-assisted quantum networks. In this stage, numerous quantum nodes capable of preparing, storing, transmitting, and manipulating quantum bits are interconnected to form large-scale quantum information networks. Thanks to the maturity of physical devices and quantum information technologies, quantum decoherence can be effectively and efficiently overcome, and the network resources are sufficient to meet the concurrent network tasks at this stage. In this stage, high-fidelity entanglement can be established between quantum terminal nodes no matter how far apart they are, thus supporting the realization of high-performance application protocols.QIN allows each quantum terminal node to arbitrarily exchange quantum information with other nodes. Similar to the current Internet, a global quantum Internet can be realized to support various quantum applications.

 

At this stage, both physical devices and quantum information technologies have been significantly improved. Therefore, the main challenge of quantum Internet is to solve the network problems such as routing design, request scheduling, resource allocation and quantum bit transmission control in order to improve the performance of entanglement-assisted quantum network so as to provide QoS service for users.

 

3) Classical communication and quantum communication

 

Entanglement-assisted quantum networks are governed by the basic laws of quantum mechanics and are fundamentally different from classical networks. In other words, entanglement-assisted quantum network is a revolutionary network rather than a development product of classical network. Entanglement-assisted quantum networks differ from classical networks in many ways. Here, the team considers a future entanglement-assisted quantum network (i.e., QIN) in its final stage of development and briefly summarizes the differences with classical networks.

 

 

A Comprehensive Comparison of Classical and Quantum Communications

 

In summary, quantum communication is fundamentally different from classical communication. Unlike classical communication, which is forwarded hop-by-hop along a classical channel, the transmission of quantum bits is not affected by quantum channel noise. In addition, due to the no- cloning theorem (no cloning theorem), quantum invisible transmission allows unconditionally secure communication, which is quite challenging in classical communication. In quantum communication, two quantum nodes must share entangled pairs of quantum bits. As long as they are entangled, quantum bits can be transmitted regardless of the distance between the communicating parties. Most notably, quantum repeaters should be used for long-distance quantum bit transmission because the signal regeneration and amplification techniques employed in classical communication cannot be used for quantum communication. Although quantum communication is superior to classical communication in terms of security, quantum communication cannot completely replace classical communication because quantum invisible state transfer is essentially a LOCC operation. Therefore, classical communication and quantum communication cooperate in entanglement-assisted quantum networks to realize quantum information transmission.

 

4) Difference with classical networks

 

As mentioned above, quantum communication is fundamentally different from classical communication. Therefore, as a promising platform that can realize quantum information transmission between arbitrary quantum nodes and support various quantum applications, entanglement-assisted quantum networks are significantly different from classical networks. Here, the team comprehensively compares entanglement-assisted quantum networks and classical networks. A detailed comparison from physical resources to protocol stacks is shown below:

 

 

Comprehensive Comparison of Entanglement-Assisted Quantum Networks and Classical Networks

 

 

The comparison between TCP/IP protocol stack and entanglement-assisted quantum network protocol stack illustrates that the protocol stack of entanglement-assisted quantum networks is significantly different from classical networks.

 

 

Representations of different protocol stacks designed for entanglement-assisted quantum networks, all four protocol stack models mentioned above recognize quantum entanglement as a key resource for entanglement-assisted quantum networks.

 

In conclusion, entanglement-assisted quantum networks are fundamentally different from classical networks. Since entanglement-assisted quantum networks are governed by the fundamental laws of quantum mechanics, while there is no corresponding law in classical networks, entanglement-assisted quantum networks have significant advantages over classical networks.

 

First, in terms of information transmission, entanglement-assisted quantum networks can realize unconditionally secure communication through the no-cloning theorem, which is difficult to realize in classical networks. In addition, the computational power of entanglement-assisted quantum networks is superior to that of classical networks. In the classical world, the computational power is limited by Moore's law. However, the superposition principle in quantum mechanics can effectively overcome the limitation of Moore's law, thus realizing the exponential growth of computing power. Therefore, entanglement-assisted quantum networks can further significantly increase computing power by interconnecting multiple quantum computers.

 

In addition, the nonlocal correlation property of quantum entanglement makes quantum sensing more accurate and sensitive than classical sensing. Although entanglement-assisted quantum networks have tremendous advantages over classical networks, their realization also faces many challenges ranging from physical resources to network design (e.g., entanglement preparation and routing design). Currently, both academic researchers and industrial practitioners are working to overcome these challenges: academic researchers are focused on designing efficient schemes to improve the performance of enabling technologies such as entanglement purification and quantum memory; industrial researchers are exploring applications of enabling technologies and developing practical physical devices. A series of breakthroughs such as long-life storage schemes and micro-quantum chips have paved the way for the construction of high-performance entanglement-assisted quantum networks with high noise immunity and high quantum bit transmission rates.

 

5) Network Elements

 

In order to support long-distance concurrent quantum bit transmission tasks, numerous quantum terminal nodes are networked with the assistance of physical channels and network devices. Therefore, the elements of entanglement-assisted quantum networks mainly include physical channels, network devices and quantum terminal nodes. In entanglement-assisted quantum networks, the network element is the entity that makes the quantum technology work.

 

 

The connection diagram between the enabling technology and the network element.

 

By employing entanglement preparation and distribution techniques, EPR sources can establish entanglement links between neighboring quantum nodes with the assistance of quantum channels. In addition, long-distance entanglement can be generated by entanglement swapping and entanglement purification of entangled quantum bit pairs stored in a quantum memory. Quantum routers or quantum repeaters can cooperate with classical channels to realize this function. After establishing end-to-end entanglement, quantum end nodes can use quantum invisible transmission state or quantum dense coding to realize high-performance information transmission with the help of quantum error correction and quantum memory.

 

 

The network elements and their functions can be briefly summarized as shown in Fig.

 

In summary, the functions of a quantum router are similar to, but more than, a quantum repeater. In addition to storing entangled quantum bits and extending the entanglement distribution distance, a quantum router needs to use local entanglement to connect entangled quantum bits from different neighbors. In short, quantum routers are responsible for extending the entanglement distribution stream from the source node to the destination node through the path chosen by the routing protocol. Currently, the fundamental research problem of quantum routing has been studied in several systems, but with many limitations. Driven by the development of physical devices, future quantum routers are expected to efficiently realize the routing of entangled distribution streams.

 

6) Network Architecture

 

Although some valuable work has explored the architecture of entanglement-assisted quantum networks, these schemes are not conducive to network scaling and protocol stack design. The differences between entanglement-assisted quantum networks and classical networks are due to the uniqueness of quantum mechanics. However, they have the same network components, except for EPR sources, and the network devices have the same functionality. For example, repeaters are deployed to extend the information transmission distance between end nodes, and quantum routers are employed to scale the network and route requests. In entanglement-assisted quantum networks, the purpose of the EPR source is to distribute entangled quantum bits between neighboring quantum nodes to provide link resources for quantum bit transmission. The EPR source coupled with the quantum channel can be analogized to the classical channel in the classical network structure. Therefore, entanglement-assisted quantum networks have a similar structure to classical networks.

 

 

General structure of wide-area entanglement-assisted quantum networks

 

Inspired by the hierarchical structure of classical networks, the team proposed a general structure for developing wide-area entanglement-assisted quantum networks. As shown in the figure, a large-scale wide-area entanglement-assisted quantum network consists of a backbone quantum network and multiple QLANs. The backbone network is an interconnection of many quantum routers, quantum repeaters, and EPR sources. More specifically, any pair of short-distance neighboring quantum routers can be directly connected via a quantum channel in concert with a classical channel. Two neighboring quantum routers that are far apart can then be connected with the help of quantum repeaters. In addition, in the backbone network, EPR sources are deployed between any pair of neighboring quantum nodes to establish entangled links. These node pairs can be repeater-to-repeater, repeater-to-router or router-to-router. The backbone network is designed for entanglement routing and establishing remote entanglement. Similar to classical LANs, quantum LANs consist of three major components: quantum information processing devices, network connecting devices and transmission media. Each quantum information device is a quantum terminal node that can handle various quantum tasks. The network connection equipment consists of quantum routers and EPR sources. In a quantum local area network (QLAN), neighboring quantum nodes are connected through the transmission medium (i.e., quantum channel and classical channel).

 

The QLAN is responsible for quantum information processing, thus providing a promising platform for various quantum applications. In wide-area entanglement-assisted quantum networks, quantum information interaction between two QLANs is realized through the backbone network.

 

7) Working Principle

 

The future entanglement-assisted quantum network works by distributing entangled quantum bit pairs between distant quantum terminal nodes and performing quantum teleportation to transmit quantum information to support various quantum applications. The implementation of end-to-end communication in entanglement-assisted quantum networks is different from that of classical networks due to significant differences in the enabling technologies.

 

 

Here, the team describes the working principle of entanglement-assisted quantum networks by taking the quantum communication between two quantum end nodes (Alice and Bob) belonging to different QLANs as an example. The figure above shows how end-to-end communication is generally realized in classical and entanglement-assisted quantum networks.

 

1) Imperfect quantum system

 

 

Imperfections of quantum systems in entanglement-assisted quantum networks.

 

The primary challenge in building future entanglement-assisted quantum networks is the inherent imperfection of quantum systems. As shown in the figure, there are many factors that lead to imperfections in quantum systems.

 

- First, in an open system, quantum bits are very fragile and therefore susceptible to noisy environments. As a result, the lifetime of a quantum bit is very short, which means that the state of a single quantum bit can only be maintained for a very short period of time after its preparation. If the state of a single quantum bit changes, the quantum information it carries is lost. In addition, quantum bits follow the non-clonability theorem. Making a copy of a single quantum bit is unlikely to reduce the effect of its short lifetime. Therefore, quantum bits need to be measured as soon as possible after they are created.

 

- Second, the photonic loss and noise inherent in quantum channels inevitably cause loss errors and quantum decoherence during quantum bit transmission, with the result that it is difficult to establish perfect entanglement links between neighboring quantum nodes.

 

- Third, although quantum memory can improve the lifetime of quantum bits, its intrinsic noise will bring redundant quantum decoherence to the quantum system. In addition, the capacity of quantum memory is limited by the incompleteness of physical devices. Therefore, it is difficult for quantum memories to operate as well as classical memories.

 

- Finally, quantum operations in entanglement-assisted quantum networks exhibit probabilistic features. For example, entanglement preparation, entanglement exchange, and entanglement purification are generally performed successfully with a certain probability. In addition, quantum operations inevitably introduce operational errors due to the inherently noisy environment of quantum hardware. As mentioned above, the inherent imperfections of quantum systems in the preparation, transmission, storage and operation of quantum bits seriously increase the difficulty of interconnecting various quantum nodes to form an entanglement-assisted quantum network with good operational performance.

 

2) Integration of various physical resources

 

Similar to classical networks, large-scale, wide-area entanglement-assisted quantum networks are usually formed by combining many heterogeneous, small-scale quantum networks. The differences between heterogeneous quantum networks are reflected in the network structure, network scale, and especially in the physical resources. In quantum information technology, various physical resources can be used to support quantum networks and interconnection networks. Physical resources vary in the preparation, transmission and storage of quantum bits. In terms of quantum bit preparation, ions, atoms, photons, spins and superconductors can all represent a quantum bit. Each of the existing forms of quantum bits has shown unique superiority in different quantum applications. For example, optical-based quantum computing technology has shown advantages in scalability and quantum coherence time, but it is not possible to program quantum bits and it is difficult to miniaturize computing devices.

 

Compared with optical quantum computing technology, quantum computing based on superconducting technology is highly maneuverable and integrable. In addition, NV color centers, trapped ions, neutral atoms, and superconducting circuits all enable the preparation of entangled quantum bits. However, quantum bits can only be transported as photons in quantum channels including optical fibers and free space. Notably, photon and matter quantum bits differ significantly. Therefore, quantum signal converters are needed to eliminate the differences between various physical resources. In conclusion, entanglement-assisted quantum networks need to provide a suitable method to abstract the underlying physical resources so as to make them globally scalable, including connecting physical and logical heterogeneous networks.

 

However, considering the imperfections of quantum systems and the no-cloning theorem, integrating various physical resources in entanglement-assisted quantum networks is quite challenging.

 

3) Synergy between classical and quantum networks

 

Entanglement-assisted quantum networks work by distributing pairs of entangled quantum bits among quantum nodes, i.e., establishing entanglement to transmit quantum bits over long distances to support breakthrough quantum applications. Notably, every quantum operation, such as entanglement swapping, entanglement purification, and quantum invisible state transfer, requires the aid of classical communication. Classical information is usually used to control the quantum operation and the feedback of the operation results.

 

Therefore, in entanglement-assisted quantum networks, cumbersome classical information interactions between quantum nodes are inevitable. The management of classical interactions directly determines whether quantum operations can be executed accurately. In addition, it is worth noting that a realistic quantum system is never completely isolated from its environment, and quantum decoherence occurs when a quantum system interacts with a noisy environment. Therefore, the additional delay associated with classical interactions between quantum nodes can negatively affect the performance of entanglement-assisted quantum networks.

 

In conclusion, entanglement-assisted quantum networks need to be effectively synergized with classical networks. However, entanglement-assisted quantum networks are governed by the laws of quantum mechanics, which have no counterpart in the classical world. Therefore, the intrinsic differences between classical and entanglement-assisted quantum networks still require further attention from researchers. In addition, security issues are also an important obstacle to the realization of entanglement-assisted quantum networks. Although the laws of quantum mechanics ensure the superiority of quantum, especially the security of quantum communication, classical communication still faces security risks. , In addition, quantum systems are so fragile that physical disturbances can seriously affect the normal operation of entanglement-assisted quantum networks, such as attacks on quantum repeaters. The security system of classical networks must be improved to ensure the security of quantum operations in entanglement-assisted quantum networks.

 

4) Relevant breakthroughs

 

Although it is challenging to construct entanglement-assisted quantum networks, the second quantum revolution has facilitated the development of quantum information technology, which has greatly spawned entanglement-assisted quantum networks.

 

 

The figure above describes some of the breakthroughs that are critical to building future entanglement-assisted quantum networks, including physical devices, enabling technologies, quantum applications, and field experiments.

 

In summary, the second quantum revolution has significantly advanced the development of quantum devices, enabling technologies and quantum applications. These breakthroughs make it possible to build entanglement-assisted quantum networks in the near future. In addition to the development of quantum hardware for building network infrastructures, network design is also a key component for realizing effective entanglement-assisted quantum networks and supporting various quantum applications.

 

This review discusses the fundamentals of quantum mechanics and demonstrates the advantages of quantum information technology, especially in terms of secure communication and enormous computing power. Entanglement-assisted quantum networks, which enable the distribution of entangled quantum bit pairs as well as the invisible transmission of quantum bits between distant quantum terminal nodes, are promising platforms for supporting breakthrough quantum applications.

 

Subsequently, the team introduces the basic enabling technologies for building future entanglement-assisted quantum networks, including entanglement preparation, quantum dense coding, entanglement switching, quantum invisible state transfer, and quantum memory, and describes the current research progress of these technologies. In addition, the team emphasizes that the development of entanglement-assisted quantum networks cannot be separated from the enabling technologies and quantum physical devices, and outlines the six stages of development of entanglement-assisted quantum networks, highlighting the capabilities of each stage. The team views entanglement-assisted quantum networks as a mesh structure consisting of a multitude of networked devices capable of quantum bit preparation, transmission, storage, and processing.

 

Existing challenges include imperfect quantum systems, integration of various physical resources, and synergy between classical and entanglement-assisted quantum networks. The team draws inspiration from classical networks to summarize research directions related to inter-network problems:

 

 

A graphical representation of the relationship between the three research directions

 

- The architectural design aims to break down the complex end-to-end quantum bit transmission problem into multiple, more tractable sub-problems. It proposes a layered protocol stack and abstracts the differences between different physical resources, thus enabling the iterative development of entanglement-assisted quantum networks.

 

- The goal of the network design is to realize a high-performance entanglement-assisted quantum network with QoS for users.The network design focuses on efficient generation and application of entanglement resources. Specifically, entanglement-ready scheduling aims to efficiently establish entanglement links between neighboring nodes to reduce remote entanglement distribution delays. Entanglement routing design is responsible for selecting a "good" path to achieve a high end-to-end entanglement establishment rate, thereby increasing the quantum bit transfer rate.

 

- Entanglement sanitization management aims to effectively improve the entanglement fidelity with less entanglement resource overhead. Entanglement exchange control is performed to efficiently establish end-to-end entanglement. Entanglement request scheduling aims to improve the utilization of entanglement link resources. Entanglement resource allocation is responsible for efficient and fair allocation of entanglement links. Congestion control aims to reduce network congestion and thus improve the quality of service of entanglement-assisted quantum networks. The standardization research promotes the development of the entanglement-assisted quantum network industry and facilitates the construction of a large-scale, wide-area quantum Internet.

 

The paper concludes with the research team saying, "We firmly believe that entanglement-assisted quantum networks will receive increasing attention from researchers and practitioners. These networks are expected to be realized in the near future, paving the way for the widespread application of quantum information technology."