Contributed Talk 5a

Abstract: 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.

Abstract: Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [GV19,Zha22]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [GV19,Zha22,GMP22], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server's operations (instead of solely the states). We introduce a new notion named *remote operator application with verifiability* (ROAV). We compare this notion with related existing definitions [SW87,MY04,MV21,NZ23], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [BGKPV], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [GV19] but also cover new state families, for example, states in the form of $\frac{1}{\sqrt{2}}(\ket{0}\ket{x_0}+\ket{1}\ket{x_1})$. All these constructions rely only on the existence of weak NTCF [BKVV,AMR22], without additional requirements like the adaptive hardcore bit property [BCMVV,AMR22]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [ABEM,Mah18] could be constructed from assumptions on group actions [ADMP20]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [AMR22], and then with the quantum-gadget-assisted quantum verification protocol [FKD18].

Abstract: High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints; thus, accessible dimensions are far exceeded by progress in HD photonics, bringing forth a need for efficient methods to compute key rates for large encoding dimensions. In response to this problem, we present a flexible analytic framework facilitated by the dual of a semi-definite program and diagonalizing operators inspired by entanglement-witness theory, enabling the efficient computation of key rates in high-dimensional systems. To facilitate the latter, we show how matrix completion techniques can be incorporated to effectively yield improved, computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond, revealing the potential for very high dimensions to surpass low dimensional protocols already with existing technology. In our accompanying work, we show how our findings can be used to establish finite-size security against coherent attacks for general HD-QKD protocols both in the fixed- and variable-length scenario and we examine the performance under realistic conditions. Detailed manuscripts for Refs. [1] and [2] can be found attached.

Abstract: We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version, and more generally, additive across tensor products of channels. For the purposes of cryptography, applying our chain rule to sequences of channels yields a new variant of R\'{e}nyi entropy accumulation, in which we can impose some specific forms of marginal-state constraint on the input states to each individual channel. This generalizes a recently introduced security proof technique that was developed to analyze prepare-and-measure QKD with no limitations on the repetition rate. In particular, our generalization yields ``fully adaptive'' protocols that can in principle update the entropy estimation procedure during the protocol itself, similar to the quantum probability estimation framework.

Abstract: Asynchronous measurement-device-independent quantum key distribution (AMDI-QKD) stands out for its experimental simplicity and high key rate generation. To simplify the system further, we devise a post-measurement compensation scheme to accurately estimate the mutual frequency offset between two compact lasers using just the announced quantum-signal detection results, thereby obviating the need for optical reference light. As a result, we demonstrate an AMDI-QKD system operating at 2.5 GHz and achieving secure key rates (SKRs) of 537 and 101 kbit/s at distances of 100 and 201 km, respectively. By leveraging ultra-stable lasers, we achieve the highest SKRs with measurement-device-independent security within the 100 to 400 km range.

Abstract: Quantum key distribution (QKD) enables information-theoretically secure communication, even in the era of quantum information. In all QKD systems, clock synchronization between two remote users---commonly referred to as Alice and Bob---is a fundamental requirement. This is typically achieved by transmitting an additional reference clock signal from Alice to Bob. In such a scheme, additional synchronization devices are required, increasing system complexity and introducing external noise. To address these issues, a novel synchronization technology, called the qubit-based synchronization method, was proposed. This method directly synchronizes two users using quantum signals, thereby dramatically reducing system complexity. However, previous qubit-based synchronization methods are not applicable to time-bin phase-encoding QKD systems, as multiple time slides introduce disturbances to time recovery. In this paper, we propose a machine-learning-enhanced qubit-based synchronization method. By introducing a K-nearest neighbor model, this method can efficiently classify each time slide in time-bin phase-encoding QKD, thereby enabling successful time recovery. We demonstrate our method using a time-bin phase-encoding reference-frame-independent (RFI)-QKD and successfully distribute secure key bits over up to 200 km of fiber spools. Our work simplifies the complexity of QKD system and significantly advances the practical application of QKD.