242 research outputs found
Exploring the Local Orthogonality Principle
Nonlocality is arguably one of the most fundamental and counterintuitive
aspects of quantum theory. Nonlocal correlations could, however, be even more
nonlocal than quantum theory allows, while still complying with basic physical
principles such as no-signaling. So why is quantum mechanics not as nonlocal as
it could be? Are there other physical or information-theoretic principles which
prohibit this? So far, the proposed answers to this question have been only
partially successful, partly because they are lacking genuinely multipartite
formulations. In Nat. Comm. 4, 2263 (2013) we introduced the principle of Local
Orthogonality (LO), an intrinsically multipartite principle which is satisfied
by quantum mechanics but is violated by non-physical correlations.
Here we further explore the LO principle, presenting new results and
explaining some of its subtleties. In particular, we show that the set of
no-signaling boxes satisfying LO is closed under wirings, present a
classification of all LO inequalities in certain scenarios, show that all
extremal tripartite boxes with two binary measurements per party violate LO,
and explain the connection between LO inequalities and unextendible product
bases.Comment: Typos corrected; data files uploade
Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation
We present a continuous-variable quantum key distribution protocol combining
a discrete modulation and reverse reconciliation. This protocol is proven
unconditionally secure and allows the distribution of secret keys over long
distances, thanks to a reverse reconciliation scheme efficient at very low
signal-to-noise ratio.Comment: 4 pages, 2 figure
Analysis of Imperfections in Practical Continuous-Variable Quantum Key Distribution
As quantum key distribution becomes a mature technology, it appears clearly
that some assumptions made in the security proofs cannot be justified in
practical implementations. This might open the door to possible side-channel
attacks. We examine several discrepancies between theoretical models and
experimental setups in the case of continuous-variable quantum key
distribution. We study in particular the impact of an imperfect modulation on
the security of Gaussian protocols and show that approximating the theoretical
Gaussian modulation with a discrete one is sufficient in practice. We also
address the issue of properly calibrating the detection setup, and in
particular the value of the shot noise. Finally, we consider the influence of
phase noise in the preparation stage of the protocol and argue that taking this
noise into account can improve the secret key rate because this source of noise
is not controlled by the eavesdropper.Comment: 4 figure
A largely self-contained and complete security proof for quantum key distribution
In this work we present a security analysis for quantum key distribution,
establishing a rigorous tradeoff between various protocol and security
parameters for a class of entanglement-based and prepare-and-measure protocols.
The goal of this paper is twofold: 1) to review and clarify the
state-of-the-art security analysis based on entropic uncertainty relations, and
2) to provide an accessible resource for researchers interested in a security
analysis of quantum cryptographic protocols that takes into account finite
resource effects. For this purpose we collect and clarify several arguments
spread in the literature on the subject with the goal of making this treatment
largely self-contained.
More precisely, we focus on a class of prepare-and-measure protocols based on
the Bennett-Brassard (BB84) protocol as well as a class of entanglement-based
protocols similar to the Bennett-Brassard-Mermin (BBM92) protocol. We carefully
formalize the different steps in these protocols, including randomization,
measurement, parameter estimation, error correction and privacy amplification,
allowing us to be mathematically precise throughout the security analysis. We
start from an operational definition of what it means for a quantum key
distribution protocol to be secure and derive simple conditions that serve as
sufficient condition for secrecy and correctness. We then derive and eventually
discuss tradeoff relations between the block length of the classical
computation, the noise tolerance, the secret key length and the security
parameters for our protocols. Our results significantly improve upon previously
reported tradeoffs.Comment: v2: completely revised, improved presentation and finite-key bounds;
v3: accepted at Quantu
Multidimensional reconciliation for continuous-variable quantum key distribution
We propose a method for extracting an errorless secret key in a
continuous-variable quantum key distribution protocol, which is based on
Gaussian modulation of coherent states and homodyne detection. The crucial
feature is an eight-dimensional reconciliation method, based on the algebraic
properties of octonions. Since the protocol does not use any postselection, it
can be proven secure against arbitrary collective attacks, by using
well-established theorems on the optimality of Gaussian attacks. By using this
new coding scheme with an appropriate signal to noise ratio, the distance for
secure continuous-variable quantum key distribution can be significantly
extended.Comment: 8 pages, 3 figure
De Finetti theorem on the CAR algebra
The symmetric states on a quasi local C*-algebra on the infinite set of
indices J are those invariant under the action of the group of the permutations
moving only a finite, but arbitrary, number of elements of J. The celebrated De
Finetti Theorem describes the structure of the symmetric states (i.e.
exchangeable probability measures) in classical probability. In the present
paper we extend De Finetti Theorem to the case of the CAR algebra, that is for
physical systems describing Fermions. Namely, after showing that a symmetric
state is automatically even under the natural action of the parity
automorphism, we prove that the compact convex set of such states is a Choquet
simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of
permutations previously described) are precisely the product states in the
sense of Araki-Moriya. In order to do that, we also prove some ergodic
properties naturally enjoyed by the symmetric states which have a
self--containing interest.Comment: 23 pages, juornal reference: Communications in Mathematical Physics,
to appea
Erratum: Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security Against Coherent Attacks [Phys. Rev. Lett. 109, 100502 (2012)]
no abstract availabl
Decision and function problems based on boson sampling
Boson sampling is a mathematical problem that is strongly believed to be
intractable for classical computers, whereas passive linear interferometers can
produce samples efficiently. So far, the problem remains a computational
curiosity, and the possible usefulness of boson-sampling devices is mainly
limited to the proof of quantum supremacy. The purpose of this work is to
investigate whether boson sampling can be used as a resource of decision and
function problems that are computationally hard, and may thus have
cryptographic applications. After the definition of a rather general
theoretical framework for the design of such problems, we discuss their
solution by means of a brute-force numerical approach, as well as by means of
non-boson samplers. Moreover, we estimate the sample sizes required for their
solution by passive linear interferometers, and it is shown that they are
independent of the size of the Hilbert space.Comment: Close to the version published in PR
Long Distance Continuous-Variable Quantum Key Distribution with a Gaussian Modulation
We designed high-efficiency error correcting codes allowing to extract an
errorless secret key in a continuous-variable quantum key distribution protocol
using a Gaussian modulation of coherent states and a homodyne detection. These
codes are available for a wide range of signal-to-noise ratios on an AWGN
channel with a binary modulation and can be combined with a multidimensional
reconciliation method proven secure against arbitrary collective attacks. This
improved reconciliation procedure considerably extends the secure range of a
continuous-variable quantum key distribution with a Gaussian modulation, giving
a secret key rate of about 10^{-3} bit per pulse at a distance of 120 km for
reasonable physical parameters.Comment: 8 pages, 5 figures, 5 table
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