State-Dependent Approach to Entropic Measurement-Disturbance Relations

Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement-disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is perfectly tight for all measurement strengths in an existing experimental setup involving qubit measurements.Comment: 9 pages, 2 figures. v4: published versio

Security of continuous-variable quantum key distribution and aspects of device-independent security

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Min- and Max-Entropy in Infinite Dimensions

We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain information-theoretic operational interpretations, e.g., the min-entropy as maximum achievable quantum correlation, and the max-entropy as decoupling accuracy. We furthermore generalize the smoothed versions of these entropies and prove an infinite-dimensional quantum asymptotic equipartition property. To facilitate these generalizations we show that the min- and max-entropy can be expressed in terms of convergent sequences of finite-dimensional min- and max-entropies, which provides a convenient technique to extend proofs from the finite to the infinite-dimensional settin

Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security against Coherent Attacks

We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for smooth entropies to give a lower bound on the number of secret bits which can be extracted from a finite number of runs of the protocol. This bound is valid under general coherent attacks, and gives rise to keys which are composably secure. For comparison, we also give a lower bound valid under the assumption of collective attacks. For both scenarios, we find positive key rates using experimental parameters reachable today.Comment: v2: new author, technical inaccuracy corrected, new plots, v3: substantially improved key rates against coherent attacks (due to correction of an error in the numerical computation

Implementation of Quantum Key Distribution with Composable Security Against Coherent Attacks using Einstein-Podolsky-Rosen Entanglement

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution (QKD) this is achieved without relying on the hardness of mathematical problems which might be compromised by improved algorithms or by future quantum computers. State-of-the-art QKD requires composable security against coherent attacks for a finite number of samples. Here, we present the first implementation of QKD satisfying this requirement and additionally achieving security which is independent of any possible flaws in the implementation of the receiver. By distributing strongly Einstein-Podolsky-Rosen entangled continuous variable (CV) light in a table-top arrangement, we generated secret keys using a highly efficient error reconciliation algorithm. Since CV encoding is compatible with conventional optical communication technology, we consider our work to be a major promotion for commercialized QKD providing composable security against the most general channel attacks.Comment: 7 pages, 3 figure

Finite-key analysis for time-energy high-dimensional quantum key distribution

Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.United States. Office of Naval Research (Grant N00014- 13-1-0774)United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052)Natural Sciences and Engineering Research Council of Canada (Postdoctoral Fellowship