1,439 research outputs found
A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
We consider two fundamental tasks in quantum information theory, data
compression with quantum side information as well as randomness extraction
against quantum side information. We characterize these tasks for general
sources using so-called one-shot entropies. We show that these
characterizations - in contrast to earlier results - enable us to derive tight
second order asymptotics for these tasks in the i.i.d. limit. More generally,
our derivation establishes a hierarchy of information quantities that can be
used to investigate information theoretic tasks in the quantum domain: The
one-shot entropies most accurately describe an operational quantity, yet they
tend to be difficult to calculate for large systems. We show that they
asymptotically agree up to logarithmic terms with entropies related to the
quantum and classical information spectrum, which are easier to calculate in
the i.i.d. limit. Our techniques also naturally yields bounds on operational
quantities for finite block lengths.Comment: See also arXiv:1208.1400, which independently derives part of our
result: the second order asymptotics for binary hypothesis testin
On the Distributed Compression of Quantum Information
The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction
Tight Finite-Key Analysis for Quantum Cryptography
Despite enormous progress both in theoretical and experimental quantum
cryptography, the security of most current implementations of quantum key
distribution is still not established rigorously. One of the main problems is
that the security of the final key is highly dependent on the number, M, of
signals exchanged between the legitimate parties. While, in any practical
implementation, M is limited by the available resources, existing security
proofs are often only valid asymptotically for unrealistically large values of
M. Here, we demonstrate that this gap between theory and practice can be
overcome using a recently developed proof technique based on the uncertainty
relation for smooth entropies. Specifically, we consider a family of
Bennett-Brassard 1984 quantum key distribution protocols and show that security
against general attacks can be guaranteed already for moderate values of M.Comment: 11 pages, 2 figure
Concise Security Bounds for Practical Decoy-State Quantum Key Distribution
Due to its ability to tolerate high channel loss, decoy-state quantum key
distribution (QKD) has been one of the main focuses within the QKD community.
Notably, several experimental groups have demonstrated that it is secure and
feasible under real-world conditions. Crucially, however, the security and
feasibility claims made by most of these experiments were obtained under the
assumption that the eavesdropper is restricted to particular types of attacks
or that the finite-key effects are neglected. Unfortunately, such assumptions
are not possible to guarantee in practice. In this work, we provide concise and
tight finite-key security bounds for practical decoy-state QKD that are valid
against general attacks.Comment: 5+3 pages and 2 figure
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