Qing-yu Cai’s research while affiliated with Hainan University and other places

In this paper, we review some methods that tried to solve the information loss problem. In particular, we revisit the solution based on Hawking radiation as tunneling, and provide a detailed statistical interpretation on the black hole entropy in terms of the quantum tunneling probability of Hawking radiation from the black hole. In addition, we show that black hole evaporation is governed by a time-dependent Schrodinger equation that sends pure states into pure states rather than into mixed states (Hawking had originally established that the final result would be mixed states). This is further confirmation of the fact that black hole evaporation is unitary.

In a perfect quantum key distribution (QKD) protocol, quantum states should be prepared and measured with mutually unbiased bases (MUBs). However, in a practical QKD system, quantum states are generally prepared and measured with imperfect MUBs using imperfect devices, possibly reducing the secret key rate and transmission distance. To analyze the security of a QKD system with imperfect MUBs, we propose virtual MUBs to characterize the quantum channel against collective attack, and analyze the corresponding secret key rate under imperfect state preparation and measurement conditions. More generally, we apply the advantage distillation method for analyzing the security of QKD with imperfect MUBs, where the error tolerance and transmission distance can be sharply improved. Our analysis method can be applied to benchmark and standardize a practical QKD system, elucidating the security analysis of different QKD protocols with imperfect devices.

In this work, we apply the advantage distillation method to improve the performance of a practical twin-field quantum key distribution system under collective attack. Compared with the previous analysis result given by Maeda, Sasaki and Koashi [Nature Communication 10, 3140 (2019)], the maximal transmission distance obtained by our analysis method will be increased from 420 km to 470 km. By increasing the loss-independent misalignment error to 12%, the previous analysis method can not overcome the rate-distance bound. However, our analysis method can still overcome the rate-distance bound when the misalignment error is 16%. More surprisingly, we prove that twin-field quantum key distribution can generate positive secure key even if the misalignment error is close to 50%, thus our analysis method can significantly improve the performance of a practical twin-field quantum key distribution system.

In order to investigate the role of quantum effects in the evolution of the universe, one can either use the Wheeler–DeWitt equation (WDWE) that contains an operator ordering factor, or add an item called massless scalar field to WDWE. In this paper, we study the relationship between operator ordering factor and massless scalar field, by applying de Broglie–Bohm quantum trajectory approach to WDWE. In theory, the evolution of the universe is determined by action, i.e., the phase part of the wavefunction of the universe. For the case of operator ordering factor and the case of massless scalar field, the functions that determine the phase part of the wavefunction of the universe satisfy the same differential equation, both in the minisuperspace model and in the Kantowski–Sachs model. This shows the equivalence of using operator ordering factor or massless scalar field to study evolution of the universe. Since there is no accelerating solution of WDWE with operator ordering factor for a grownup universe in the minisuperspace model, the equivalence of the operator ordering factor and the massless scalar field rules out the possibility of a massless scalar field as the candidate for dark energy, if the current universe is indeed homogeneous and isotropic.

Quantum key distribution can provide information-theoretic security keys. In practice, the eavesdropper may attack the transmitted quantum state, which makes some information leakage to the generated key. The security of the final key depends on how difficult it is for the eavesdropper to guess the key. The guessing probability is bounded by the trace distance between the practical generated quantum state and the ideal quantum state and hence can be applied to estimate security of quantum key distribution. With the trace distance ε$\varepsilon$ and the secret key length n, we prove that the guessing probability can reach the upper bound ε+2-n$\varepsilon +2^{-n}$ in some special cases. We show that different attacking strategies will give different numbers of guesses, sometimes even completely subversive differences, to get the final key. Our results demonstrate that the appropriate security parameter ε$\varepsilon$ should be carefully selected to guarantee the security of the generated key.

Quantum key distribution (QKD) provides a promising solution for sharing information-theoretic secret keys between two remote legitimate parties. To improve the maximal transmission distance and the maximal error rate tolerance, we apply the advantage distillation technology to analyze the security of practical decoy-state QKD systems. Based on the practical experimental parameters, the device-dependent QKD protocols and the measurement-device-independent QKD protocols have been respectively analyzed, and our analysis results demonstrate that the advantage distillation technology can significantly improve the performance of various QKD protocols. In the four-state and six-state device-dependent QKD protocols, we prove that the maximal transmission distance can be improved from 142 km to 180 km and from 146 km to 187 km respectively. In the four-state and six-state measurement-device-independent QKD protocols, we prove that the maximal transmission distance can be improved from 195 km to 273 km and from 200 km to 282 km respectively. Advantage distillation technology increases the collection between raw keys in quantum key distribution systems. Combining a decoy state method with advantage distillation technology, the authors demonstrate improved maximal transmission distance and tolerable background error rates.

In this work, we apply two methods to improve performance of a practical twin-field quantum key distribution system. Firstly, to improve the secure key rate, we apply the error rate in X basis, Y basis and Z basis to precisely characterize the quantum channel. Secondly, we apply the advantage distillation method to further improve the secure key rate and the secure key transmission distance. Compared with the previous analysis result given by Maeda, Sasaki and Koashi [Nature Communication 10, 3140 (2019)], the secure key rate obtained by our analysis method will be increased at least 7%. By increasing the loss-independent misalignment error to 12%, the previous analysis method can not overcome the rate-distance bound. However, our analysis method can still overcome the rate-distance bound when the misalignment error is as large as 41%. More surprisingly, we prove that twin-field quantum key distribution can generate positive secure key even if the misalignment error arbitrary close to 50%, thus our analysis method can significantly improve the performance of a practical twin-field quantum key distribution system.

Quantum algorithms can greatly speed up computation in solving some classical problems, while the computational power of quantum computers should also be restricted by laws of physics. Due to quantum time-energy uncertainty relation, there is a lower limit of the evolution time for a given quantum operation, and therefore the time complexity must be considered when the number of serial quantum operations is particularly large. When the key length is about at the level of KB (encryption and decryption can be completed in a few minutes by using standard programs), it will take at least 50-100 years for NTC (Neighbor-only, Two-qubit gate, Concurrent) architecture ion-trap quantum computers to execute Shor’s algorithm. For NTC architecture superconducting quantum computers with a code distance 27 for error-correcting, when the key length increased to 16 KB, the cracking time will also increase to 100 years that far exceeds the coherence time. This shows the robustness of the updated RSA against practical quantum computing attacks.

To improve the maximal transmission distance and the maximal error rate tolerance, we apply the advantage distillation technology to analyze security of the practical decoy-sate quantum key distribution system. Based on the practical experimental parameters, the device-dependent quantum key distribution protocols and the measurement-device-independent quantum key distribution protocols have been respectively analyzed, and our analysis results demonstrate that the advantage distillation technology can significantly improve the performance of different quantum key distribution protocols. In the four-state and six-state device-dependent quantum key distribution protocols, we prove that the maximal transmission distance can be improved from 142 km to 180 km and from 146 km to 187 km respectively. In the four-state and six-state measurement-device-independent quantum key distribution protocols, we prove that the maximal transmission distance can be improved from 195 km to 273 km and from 200 km to 282 km respectively. More interestingly, the advantage distillation technology does not need to change the hardware devices about the quantum step, thus it can be conveniently to be applied in various practical quantum key distribution systems.