Xingjian Zhang

In the recent breakthrough result (Mastel and Slofstra, STOC24), the authors show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE. We build on their result to show that there exists a succinct two-player one-round perfect zero-knowledge MIP* protocol for RE with polylog question size and O(1) answer size, or with O(1) question size and polylog answer size. To prove our result, we analyze the four central compression techniques underlying the MIP*=RE proof (Ji et al., arXiv:2001.04383) --- question reduction, oracularization, answer reduction, and parallel repetition --- and show that they all preserve the perfect (as well as statistical and computational) zero-knowledge properties of the original protocol. Furthermore, we complete the study of the conversion between constraint-constraint and constraint-variable binary constraint system (BCS) nonlocal games, which provide a quantum information characterization of MIP* protocols. While Paddock (arXiv:2203.02525) established that any near perfect strategy for a constraint-variable game can be mapped to a constraint-constraint version, we prove the converse, fully establishing their equivalence.

Quantum error mitigation is a key approach for extracting target state properties on state-of-the-art noisy machines and early fault-tolerant devices. Using the ideas from flag fault tolerance and virtual state purification, we develop the virtual channel purification (VCP) protocol, which consumes similar qubit and gate resources as virtual state purification but offers up to exponentially stronger error suppression with increased system size and more noisy operation copies. Furthermore, VCP removes most of the assumptions required in virtual state purification. Essentially, VCP is the first quantum error mitigation protocol that does not require specific knowledge about the noise models, the target quantum state, and the target problem while still offering rigorous performance guarantees for practical noise regimes. Further connections are made between VCP and quantum error correction to produce one of the first protocols that combine quantum error correction and quantum error mitigation beyond concatenation. We can remove all noise in the channel while paying only the same sampling cost as low-order purification, reaching beyond the standard bias-variance trade-off in quantum error mitigation. Our protocol can also be adapted to key tasks in quantum networks like channel capacity activation and entanglement distribution.

Recent advances in loophole-free Bell tests have profoundly impacted quantum cryptography, yet their security assumes trusted random number generators (RNGs) for measurement choices—a vulnerability termed the freedom-of-choice loophole. Here, we demonstrate that classical systems can spoof Bell violations under ostensibly loophole-free conditions using compromised RNGs. By synchronizing laser-generated separable states with imperfect RNG outputs in an optical setup, we simulate a CHSH test closing locality and detection loopholes. With full RNG access, we achieve a near-maximal CHSH value of 3.99, exceeding quantum limits. Crucially, partial RNG knowledge suffices: predetermining 10.6% of bits reproduces our “loophole free” optical system's CHSH value of 2.007, while Santha-Vazirani generators with 0.38-biased bits enable optimal spoofing. Even weakly correlated RNGs coordinated via entangled states—deviating by 0.04 from independence—allow violations. Prediction-based ratio analysis gives a P-value upper bound of 10^(-18266), misleadingly implying non-classicality if RNG flaws are ignored. Strikingly, we extract "device-independent" random bits from simulated outcomes, mirroring cryptographic protocols. This exposes a critical flaw: compromised input randomness invalidates security guarantees in Bell-inequality-based cryptography. Our findings mandate rigorous verification of both RNG integrity and Bell violations to ensure quantum cryptographic security.

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.

Continuous-variable quantum key distribution (CV QKD) using optical coherent detectors is practically favorable due to its low implementation cost, flexibility of wavelength division multiplexing, and compatibility with standard coherent communication technologies. However, the security analysis and parameter estimation of CV QKD are complicated due to the infinite-dimensional latent Hilbert space. Also, the transmission of strong reference pulses undermines the security and complicates the experiments. In this work, we tackle these two problems by presenting a time-bin-encoding CV protocol with a simple phase-error-based security analysis valid under general coherent attacks. With the key encoded into the relative intensity between two optical modes, the need for global references is removed. Furthermore, phase randomization can be introduced to decouple the security analysis of different photon-number components. We can hence tag the photon number for each round, effectively estimate the associated privacy using a carefully designed coherent-detection method, and independently extract encryption keys from each component. Simulations manifest that the protocol using multi-photon components increases the key rate by two orders of magnitude compared to the one using only the single-photon component. Meanwhile, the protocol with four-intensity decoy analysis is sufficient to yield tight parameter estimation with a short-distance key-rate performance comparable to the best Bennett-Brassard-1984 (BB84) implementation.