Xiongfeng Ma

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this work, we rigorously prove through information-theoretic analysis that one-dimensional logarithmic-depth random Clifford encoding circuits can achieve high quantum error correction performance. We demonstrate that these random codes typically exhibit good approximate quantum error correction capability by proving that their encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors. We show that the error correction inaccuracy decays once a threshold of logarithmic depth is exceeded, resulting in negligible recovery errors. This threshold is shown to be lower than that of the simple separate block encoding, and the decay rate is higher. We further establish that these codes are optimal by proving that logarithmic depth is necessary to maintain a constant encoding rate and high error correction performance. To prove our results, we propose new decoupling theorems for one-dimensional low-depth circuits. These results also imply strong decoupling and rapid thermalization properties in low-depth random circuits and have potential applications in quantum information science and physics.

We demonstrate a practical high-performance mode-pairing quantum key distribution system that is able to surpass the repeaterless key rate bound using commercial lasers. We propose a frequency tracking scheme to address phase fluctuations and a theoretical model to analyze the phase noise and optimize the system parameters. Our system achieves a secret key rate of 47.8 bit/s over 403 km standard fiber, which is 2.92 times of the repeaterless bound. Furthermore, we compare the performance between MP-QKD and no-phase-locking TF-QKD under various practical conditions and show that MP-QKD exhibits superior performance at short distances with low error rates, while TF-QKD is more advantageous for long distances with consistent error rates.

Quantum key distribution is a cornerstone of quantum technology, offering information-theoretical secure keys for remote parties. With many quantum communication networks established globally, the mode-pairing protocol stands out for its efficacy over inter-city distances using simple setups, emerging as a promising solution. In this study, we employ the mode-pairing scheme into existing inter-city fiber links, conducting field tests across distances ranging from tens to about a hundred kilometers. Our system achieves a key rate of $1.217$ kbit/s in a $195.85$ km symmetric link and $3.089$ kbit/s in a $127.92$ km asymmetric link without global phase locking. The results demonstrate that the mode-pairing protocol can achieve key rates comparable to those of a single quantum link between two trusted nodes on the Beijing-Shanghai backbone line, effectively reducing the need for half of the trusted nodes. These field tests confirm the mode-pairing scheme's adaptability, efficiency, and practicality, positioning it as a highly suitable protocol for quantum networks.

Enhancing the performance of quantum key distribution is crucial, driving the exploration of various key distillation techniques to increase the key rate and tolerable error rate. It is imperative to develop a comprehensive framework to encapsulate and enhance the existing methods. In this work, we propose an advantage distillation framework for quantum key distribution. Building on the entanglement distillation protocol, our framework integrates all the existing key distillation methods and offers better generalization and performance. Using classical linear codes, our framework can achieve higher key rates, particularly without one-time pad encryption for postprocessing. Our approach provides insights into existing protocols and offers a systematic way for future enhancements of quantum key distribution protocols.

Quantum key distribution stands as a cornerstone of quantum information science, enabling secure communication based on fundamental quantum principles. In reality, practical implementations often rely on the decoy-state method to ensure security against photon-number-splitting attacks. A significant challenge in realistic quantum cryptosystems arises from statistical fluctuations due to finite data sizes, which complicate the key-rate estimation because of the nonlinear dependence on the phase error rate. In this study, we refine and enhance the key rate bound for the decoy-state method and introduce an improved statistical fluctuation analysis framework. By integrating our refined bound with this advanced fluctuation analysis, we achieve higher key generation rates, as demonstrated in numerical simulations of the one-decoy-state method --- a simple yet increasingly practical protocol --- under typical experimental conditions. Notably, our approach to fluctuation analysis extends beyond quantum cryptography, offering broad applicability to various quantum information processing tasks, particularly those involving linear relationships between objectives and experimental variables.