50 research outputs found
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
[no abstract
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
Optimality of entropic uncertainty relations
The entropic uncertainty relation proven by Maassen and Uffink for arbitrary
pairs of two observables is known to be non-optimal. Here, we call an
uncertainty relation optimal, if the lower bound can be attained for any value
of either of the corresponding uncertainties. In this work we establish optimal
uncertainty relations by characterising the optimal lower bound in scenarios
similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al.
and generalise various previous results. However, we are still far from a
complete understanding and, based on numerical investigation and analytical
results in small dimension, we present a number of conjectures.Comment: 24 pages, 10 figure