SUSTech undergraduate PRL paper realizes quantum refrigerator driven by indeterminate causal order

Recently, a quantum refrigerator driven by indefinite causal orders has been experimentally realized by the physics faculty and students of Southern University of Science and Technology. The results were published in Physical Review Letters under the title "Experimental realization of a quantum refrigerator driven by indefinite causal orders". Review Letters.

Cause and effect is a fundamental concept in our understanding of the world and is the basis of the concept of time. It plays a crucial role in our cognition, enabling us to determine the causes of certain events, to make scientific predictions about the future, and to choose appropriate behaviors to achieve our goals. However, when we step into the quantum world, it is possible that the causal order of events becomes less certain. For example, there may be an indeterminate causal order, corresponding to a quantum superposition of "A leads to B" and "B leads to A".

Schematic representation of indeterminate causal order (J. Schmöle)

Physicist Giulia Rubino and colleagues have experimentally demonstrated that causal order in the quantum world can indeed become indeterminate. The quantum superposition of the causal order of gate operations is achieved by a construction called the quantum switch, in which a single photon state is used to control the sequence of action of a logic gate. Finally, a "Causal Witness" is measured at the output to determine whether the process is causally established.

Schematic diagram of the quantum superposition of the causal order of gate operations (from Giulia Rubino's experimental article)

The thermodynamic process experienced by a certain target object can also be seen as a series of probabilistic actions of gates, and we can implement a similar approach for the indefinite causal order of the thermodynamic process. According to the second law of thermodynamics, heat will only be transferred spontaneously from a high temperature object to a low temperature object, and no heat transfer will occur when two objects of the same temperature are placed together. In other words, if we refer to a target object in thermal contact with a heat source of the same temperature as event A and another heat source of the same temperature as event B, the order in which A and B occur does not affect the final temperature of the target object, and the temperature of the target object always remains the same during the process. In the classical world, this is a very banal conclusion.

However, surprisingly, physicists Felce and Vedral found that when we arrange the two thermodynamic processes A and B in an indeterminate causal order, the final temperature of the target object may increase or decrease by questioning the "causal witness". This may seem to violate the second law of thermodynamics, but in fact, this phenomenon is similar to the "Maxwell demon" paradox, which does not violate the second law of thermodynamics, the most fundamental physical law, and the "causal witness" is The "causal witness" is the equivalent of the mischievous leprechaun who keeps observing and remembering. In a thermal contact of indeterminate causal order, the change in entropy comes from the observation of the "causal witness", i.e., the leprechaun. The entropy of the system does not decrease spontaneously if the leprechaun is included in the system. In this process, we can see the quantum heat exchange effect, and through this amazing phenomenon, we can realize a quantum refrigerator based on the principle of indefinite causal order.

In the sample, the researchers used the fluorine element in the upper left corner as the working bit, the carbon element in the middle as the control bit, and the two fluorine elements below as the heat reservoir. The final observed state of the control bits determines the direction of the heat flow, and using this property, the researchers achieved a quantum refrigerator based on an indefinite causal order.

The researchers conducted experiments on a nuclear magnetic resonance quantum simulator to demonstrate for the first time the amazing thermodynamic properties of the indeterminate causal order process on a system of four nuclear spin quantum bits. The researchers used the carbon nucleus of the four nuclei as the "causal witness," a fluorine nucleus as the working matter of the refrigerator, and the other two fluorine nuclei as the heat source at the same temperature as the working matter. The order of contact between the working substance and the two heat sources is controlled by preparing the "causal witnesses" to different states. When the "causal witness" is in |0> or |1>, the working substance will contact with heat source 1 (event A) and heat source 2 (event B) in a fixed order; when the "causal witness" is in the quantum superposition of |0> and |1>, the working substance When the "causal witness" is in a quantum superposition of |0> and |1>, the working substance will be in contact with the heat source in an indeterminate causal order, i.e. a quantum version of the refrigerator. Finally, when the "causal witness" is at |0>-|1>, the working matter will absorb heat from the heat source, i.e., the cooling effect of the "refrigerator" can be achieved; conversely, when it is at |0>+|1>, the working matter will exert heat to the heat source. . In other words, even if the working substance and the two heat sources are always at the same temperature, the heat transfer effect can still occur in the case of thermal contact of indeterminate causal order.

Next, using this property of indeterminate causal order, the researchers designed a four-stroke quantum refrigerator as shown in the figure below: (1) the working substance is in thermal contact with two low-temperature heat sources in an indeterminate causal order, and then the "causal witness" (goblin) is measured. The "causal witness" makes a judgment on the measurement result. When the result is |0>-|1>, the thermodynamic cycle continues; conversely, process (1) continues until the measurement result is |0>-|1>; (2) the working substance is exposed to a high-temperature heat source and exothermic; (3) the working substance is exposed to a low-temperature heat source and exothermic; and (4) the "causal witness" and the working substance are initialized. The researchers focused on the energy transfer, the probability of success of the refrigerator experiment, and the efficiency of the process.

A four-stroke quantum refrigerator based on thermal contact with an indeterminate causal sequence.

In an experimental study of a refrigerator based on an indeterminate causal sequence, the researchers found that the efficiency of the refrigerator is limited by the probability of success of the "causal witness" measurement in process (1) and is always limited to a small value (about 0.08). To improve the efficiency of the refrigerator, the researchers proposed a framework based on Density matrix exponentiation. This approach increased the efficiency of the refrigerator by a factor of 3 and was experimentally validated. This work successfully demonstrates a non-classical heat exchange interaction based on an indefinite causal order, paving the way for more research on quantum refrigerators in the future.

(a) Curves of the work consumed and heat transfer occurring in a single cycle with respect to temperature (b) Comparison of the efficiency of the original indefinite causal order refrigerator (ICO) and the refrigerator based on the density matrix exponentiation framework (DME) at different temperatures. It can be seen that the efficiency of the "quantum refrigerator" has been significantly improved.

Xinfang Nie, a research assistant professor in the Department of Physics at Southern University of Science and Technology, and Xianran Zhu, a 2017 undergraduate student in the Department of Physics (currently pursuing his PhD at the Hong Kong University of Science and Technology), are the co-first authors of the paper. The work was completed during his junior year, when he joined Lu Dawei's group at SUSTech to conduct quantum computing research, focusing on quantum heat machines and quantum simulation of topological states. He was a key contributor to the successful completion of the project, as he led the theoretical numerical simulations, designed the experimental scheme, and wrote the paper. Dawei Lu's group has always paid great attention to the scientific training of undergraduates, "tailoring" the training to the students' characteristics, and encouraging and supporting students to explore the most interesting research directions.

Collaborators on this work include Ying Dong, a researcher at Zhijiang Laboratory, Jun Li, a researcher at the Institute of Quantum Science and Engineering, and Tao Xin, an associate researcher. Ying Dong, Tao Xin, and Dawei Lu are co-corresponding authors, and SUSTech is the first author of the paper. The research was supported by the Ministry of Science and Technology, the National Natural Science Foundation of China, the Department of Science and Technology of Guangdong Province, the Shenzhen Science and Technology Commission, the Southern University of Science and Technology, and the Zhijiang Laboratory.

Link to the paper：

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.100603