Imperfect Phase-Randomisation and Generalised Decoy-State Quantum Key Distribution

Decoy-state methods [1, 2] are essential to perform quantum key distribution (QKD) at large distances in the absence of single photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed (iid). Moreover, they require that the laser pulses are fully phase-randomised. However, realistic high-speed QKD setups do not meet these stringent requirements [3]. In this work, we generalise decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomised states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [4] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase-randomisation on key rates by computing the key rates for a simple implementation of the three-state protocol

Lift & Project Systems Performing on the Partial-Vertex-Cover Polytope

We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the Sherali-Adams (SA), Lovasz-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC) problem, a variation of the classic Vertex-Cover problem in which only t edges need to be covered. t-PVC admits a 2-approximation using various algorithmic techniques, all relying on a natural LP relaxation. Starting from this LP relaxation, our main results assert that for every epsilon > 0, level-Theta(n) LPs or SDPs derived by all known L&P systems that have been used for positive algorithmic results (but the Lasserre hierarchy) have IGs at least (1-epsilon)n/t, where n is the number of vertices of the input graph. Our lower bounds are nearly tight. Our results show that restricted yet powerful models of computation derived by many L&P systems fail to witness c-approximate solutions to t-PVC for any constant c, and for t = O(n). This is one of the very few known examples of an intractable combinatorial optimization problem for which LP-based algorithms induce a constant approximation ratio, still lift-and-project LP and SDP tightenings of the same LP have unbounded IGs. We also show that the SDP that has given the best algorithm known for t-PVC has integrality gap n/t on instances that can be solved by the level-1 LP relaxation derived by the LS system. This constitutes another rare phenomenon where (even in specific instances) a static LP outperforms an SDP that has been used for the best approximation guarantee for the problem at hand. Finally, one of our main contributions is that we make explicit of a new and simple methodology of constructing solutions to LP relaxations that almost trivially satisfy constraints derived by all SDP L&P systems known to be useful for algorithmic positive results (except the La system).Comment: 26 page

Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols

Discrete-Modulated (DM) Continuous-Variable Quantum Key Distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed (i.i.d.) collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's epsilon-security framework. We introduce and build up our security argument on so-called acceptance testing which, as we argue, is the proper notion for the statistical analysis in the finite-size regime and replaces the concept of parameter estimation for asymptotic security analyses. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol, both for untrusted, ideal and trusted non-ideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 73 km transmission distance.Comment: 28 pages, 6 Figure

Noncommuting conserved charges in quantum thermodynamics and beyond

Thermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables' failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges' noncommutation has been found to invalidate derivations of the thermal state's form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.Comment: 9.5 pages (3 figures) + appendices (10 pages

Tools for the Security Analysis of Quantum Key Distribution in Infinite Dimensions

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols