Beijing Quantum Institute makes new progress in high-dimensional one-way quantum guidance research

Recently, Zeng Qiang, an assistant researcher in the optical quantum communication and device team of the Department of Quantum Materials and Devices, Beijing Institute of Quantum Research, has completed a preliminary study of the one-way quantum steering effect in high dimensions. The results, entitled "One-way Einstein-Podolsky-Rosen steering beyond qubits", were published in Physical Review A on September 2, 2022.

The concept of quantum entangled states began with the well-known Einstein-Podolsky-Rosen (EPR) feint, which describes the strongly correlated nature of a class of two-body systems exhibiting space-like partitions. Although quantum entangled states have a well-defined mathematical structure, they are regarded as a counterintuitive presence in real physical systems. The discussion of quantum entangled states was only at the level of thought experiments until 1965 when Bell proposed a feasible experimental verification scheme, namely Bell's inequality.

Subsequently, it was discovered that for two-body systems, there exists a new class of entangled structures between those satisfying the most basic structure of entangled states (i.e., indistinguishable) and those violating Bell's inequality, which assigns different forms to the two subsystems and thus has a non-symmetric character in its definition. Based on this feature, it is named quantum steering, which reflects the distinction between the steerer and the steered when "steering". It has been shown that for a given quantum state, if at least one party can guide the other, the quantum state must be entangled; moreover, if the quantum state can violate Bell's inequality, both parties involved in the entanglement must be able to guide each other.

Fig. 1 Unidirectional guided quantum state and bidirectional guided quantum state

Quantum guidance as a class of entangled structures has a wide range of applications in single-sided device-independent key distribution, random number verification, sub-channel identification and secret sharing. In particular, it is used in improving the noise tolerance of quantum channels. Recent research results show that the single-sided device-independent scheme can fundamentally solve the problem of detecting vulnerabilities compared to the traditional E91 bilateral device-independent scheme.

In this work, the authors first propose a class of high-dimensional entangled states with one-way quantum-guided properties. Then the parameter range of the unidirectional guiding effect is given quantitatively by numerical methods for dimension 3 under unbiased basis measurements and generalized measurements.

Figure 2 Left: Unbiased measurement results; Right: Generalized measurement results

In addition, the authors propose a new noise model based on the previously proposed "a priori measurement set" and quantify the relationship between quantum channel noise and quantum state entanglement (Figure 3). The results are significantly better at low noise compared to the existing results.

Fig. 3 Quantum channel noise versus the degree of entanglement of quantum states

Finally, using this noise model, the authors quantitatively give the trade-off between the 3-dimensional one-way quantum guided state channel noise and the number of measurement basis vectors (Figure 4). Also, the noise model can be used for the case of finite dimensionality and finite number of measurement basis vectors within the arithmetic power allowed.

 Fig. 4 Check and balance between channel noise and number of measured basis vectors for 3-dimensional one-way quantum guided states

This work was supported by the National Natural Science Foundation of China and the Postdoctoral International Exchange Program.