23 research outputs found
Sequential decoding of a general classical-quantum channel
Since a quantum measurement generally disturbs the state of a quantum system,
one might think that it should not be possible for a sender and receiver to
communicate reliably when the receiver performs a large number of sequential
measurements to determine the message of the sender. We show here that this
intuition is not true, by demonstrating that a sequential decoding strategy
works well even in the most general "one-shot" regime, where we are given a
single instance of a channel and wish to determine the maximal number of bits
that can be communicated up to a small failure probability. This result follows
by generalizing a non-commutative union bound to apply for a sequence of
general measurements. We also demonstrate two ways in which a receiver can
recover a state close to the original state after it has been decoded by a
sequence of measurements that each succeed with high probability. The second of
these methods will be useful in realizing an efficient decoder for fully
quantum polar codes, should a method ever be found to realize an efficient
decoder for classical-quantum polar codes.Comment: 12 pages; accepted for publication in the Proceedings of the Royal
Society
Quantum key distribution with finite resources: Taking advantage of quantum noise
We compare the effect of different noise scenarios on the achievable rate of
an epsilon-secure key for the BB84 and the six-state protocol. We study the
situation where quantum noise is added deliberately, and investigate the
remarkable benefit for the finite key rate. We compare our results to the known
case of added classical noise and the asymptotic key rate, i.e. in the limit of
infinitely many signals. As a complementary interpretation we show that under
the realistic assumption that the noise which is unavoidably introduced by a
real channel is not fully dedicated to the eavesdropper, the secret key rate
increases significantly.Comment: 14 pages, 8 figure
Duality of privacy amplification against quantum adversaries and data compression with quantum side information
We show that the tasks of privacy amplification against quantum adversaries
and data compression with quantum side information are dual in the sense that
the ability to perform one implies the ability to perform the other. These are
two of the most important primitives in classical information theory, and are
shown to be connected by complementarity and the uncertainty principle in the
quantum setting. Applications include a new uncertainty principle formulated in
terms of smooth min- and max-entropies, as well as new conditions for
approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for
smooth min- and max-entropies. Discussion of the
Holevo-Schumacher-Westmoreland theorem remove
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
The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
The Quantum Reverse Shannon Theorem states that any quantum channel can be
simulated by an unlimited amount of shared entanglement and an amount of
classical communication equal to the channel's entanglement assisted classical
capacity. In this paper, we provide a new proof of this theorem, which has
previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof
has a clear structure being based on two recent information-theoretic results:
one-shot Quantum State Merging and the Post-Selection Technique for quantum
channels.Comment: 30 pages, 4 figures, published versio
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