Physics(ish) (Chair: Joseph Slote)

Abstract: In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between smooth min-entropy and smooth max-information, which improves over previous chain rules for characterizing one-shot information leakage caused by an additional conditioning register. Second, we derive an information accumulation theorem that bounds the Rényi mutual information of a state produced by a sequence of channels, in terms of the Rényi mutual information of the individual channel outputs. In particular, this yields simple bounds on the smooth max-information in the preceding chain rule. Third, we derive chain rules between Rényi entropies and Rényi mutual information, which can be used to modify the entropy accumulation theorem to accommodate leakage registers sent to the adversary in each round of a protocol. We show that these results can be used to handle some device imperfections in a variety of device-dependent and device-independent protocols, such as randomness generation and quantum key distribution.

Abstract: We developed new concentration inequalities for a quantum state on an N -qudit system or measurement outcomes on it that apply to an adversarial setup, where an adversary prepares the quantum state. Our one-sided concentration inequalities for a quantum state require the N -qudit system to be permutation invariant and are thus de-Finetti type, but they are tighter than the one previously obtained. We show that the bound can further be tightened if each qudit system has an additional symmetry. Furthermore, our concentration inequality for the outcomes of independent and identical measurements on an N -qudit quantum system has no assumption on the adversarial quantum state and is much tighter than the conventional one obtained through Azuma’s inequality. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.

Abstract: We present a security proof for variable-length QKD against IID collective attacks. Our proof can be lifted to coherent attacks using the postselection technique. Our first main result is a theorem to convert a sequence of security proofs for fixed-length protocols satisfying certain conditions to a security proof for a variable-length protocol. This conversion requires no new calculations, does not require any changes to the final key lengths or the amount of error-correction information, and at most doubles the security parameter. Our second main result is the description and security proof of a more general class of variable-length QKD protocols, which does not require characterizing the honest behaviour of the channel connecting the users before the execution of the QKD protocol. Instead, these protocols adaptively determine the length of the final key, and the amount of information to be used for error-correction, based upon the observations made during the protocol. We apply these results to the qubit BB84 protocol, and show that variable-length implementations lead to higher expected key rates than the fixed-length implementations. Finally, we point out a critical flaw in the analysis of privacy amplification that arises due to sifting. We provide an elegant solution that retroactively fixes this flaw.

Abstract: Security proofs for quantum key distribution (QKD) based on the entropic uncertainty relations and the phase-error approach have the advantage of producing some of the tightest key rates against coherent attacks. We prove the security of QKD using the entropic uncertainty relations, for scenarios where Eve is allowed full control of the detection efficiency and dark rates of all detectors within some specified ranges. Thus, our work solves the practically important problem of detector side channels. Our work also removes the requirement of ``basis-independent loss'' required by these proof techniques. Thus, we render these proof techniques applicable to practical QKD scenarios. Furthermore, we prove security for variable-length QKD protocols, which do not require Alice and Bob to characterize the honest behaviour of the channel.

Abstract: Quantum key distribution (QKD) promises everlasting security based on the laws of physics. Most common protocols are grouped into two distinct categories based on the degrees of freedom used to carry information, which can be either discrete or continuous, each presenting unique advantages in either performance, feasibility for near-term implementation, and compatibility with existing telecommunications architectures. Recently, hybrid QKD protocols have been introduced to leverage advantages from both categories. In this work we provide a rigorous security proof for a protocol introduced by Qi in 2021, where information is encoded in discrete variables as in the widespread Bennett Brassard 1984 (BB84) protocol but decoded continuously via heterodyne detection. Security proofs for hybrid protocols inherit the same challenges associated with continuous-variable protocols due to unbounded dimensions. Here we successfully address these challenges by exploiting symmetry. Our approach enables truncation of the Hilbert space with precise control of the approximation errors and lead to a tight, semi-analytical expression for the asymptotic key rate under collective attacks. As concrete examples, we apply our theory to compute the key rates under passive attacks, linear loss, and Gaussian noise.