133,857 research outputs found
Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
A strong converse theorem for the classical capacity of a quantum channel
states that the probability of correctly decoding a classical message converges
exponentially fast to zero in the limit of many channel uses if the rate of
communication exceeds the classical capacity of the channel. Along with a
corresponding achievability statement for rates below the capacity, such a
strong converse theorem enhances our understanding of the capacity as a very
sharp dividing line between achievable and unachievable rates of communication.
Here, we show that such a strong converse theorem holds for the classical
capacity of all entanglement-breaking channels and all Hadamard channels (the
complementary channels of the former). These results follow by bounding the
success probability in terms of a "sandwiched" Renyi relative entropy, by
showing that this quantity is subadditive for all entanglement-breaking and
Hadamard channels, and by relating this quantity to the Holevo capacity. Prior
results regarding strong converse theorems for particular covariant channels
emerge as a special case of our results.Comment: 33 pages; v4: minor changes throughout, accepted for publication in
Communications in Mathematical Physic
Smooth Entropy Bounds on One-Shot Quantum State Redistribution
In quantum state redistribution as introduced in [Luo and Devetak (2009)] and
[Devetak and Yard (2008)], there are four systems of interest: the system
held by Alice, the system held by Bob, the system that is to be
transmitted from Alice to Bob, and the system that holds a purification of
the state in the registers. We give upper and lower bounds on the amount
of quantum communication and entanglement required to perform the task of
quantum state redistribution in a one-shot setting. Our bounds are in terms of
the smooth conditional min- and max-entropy, and the smooth max-information.
The protocol for the upper bound has a clear structure, building on the work
[Oppenheim (2008)]: it decomposes the quantum state redistribution task into
two simpler quantum state merging tasks by introducing a coherent relay. In the
independent and identical (iid) asymptotic limit our bounds for the quantum
communication cost converge to the quantum conditional mutual information
, and our bounds for the total cost converge to the conditional
entropy . This yields an alternative proof of optimality of these rates
for quantum state redistribution in the iid asymptotic limit. In particular, we
obtain a strong converse for quantum state redistribution, which even holds
when allowing for feedback.Comment: v3: 29 pages, 1 figure, extended strong converse discussio
Lecture Notes on Network Information Theory
These lecture notes have been converted to a book titled Network Information
Theory published recently by Cambridge University Press. This book provides a
significantly expanded exposition of the material in the lecture notes as well
as problems and bibliographic notes at the end of each chapter. The authors are
currently preparing a set of slides based on the book that will be posted in
the second half of 2012. More information about the book can be found at
http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of
the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/
The invalidity of a strong capacity for a quantum channel with memory
The strong capacity of a particular channel can be interpreted as a sharp
limit on the amount of information which can be transmitted reliably over that
channel. To evaluate the strong capacity of a particular channel one must prove
both the direct part of the channel coding theorem and the strong converse for
the channel. Here we consider the strong converse theorem for the periodic
quantum channel and show some rather surprising results. We first show that the
strong converse does not hold in general for this channel and therefore the
channel does not have a strong capacity. Instead, we find that there is a scale
of capacities corresponding to error probabilities between integer multiples of
the inverse of the periodicity of the channel. A similar scale also exists for
the random channel.Comment: 7 pages, double column. Comments welcome. Repeated equation removed
and one reference adde
Strong converse rates for classical communication over thermal and additive noise bosonic channels
We prove that several known upper bounds on the classical capacity of thermal
and additive noise bosonic channels are actually strong converse rates. Our
results strengthen the interpretation of these upper bounds, in the sense that
we now know that the probability of correctly decoding a classical message
rapidly converges to zero in the limit of many channel uses if the
communication rate exceeds these upper bounds. In order for these theorems to
hold, we need to impose a maximum photon number constraint on the states input
to the channel (the strong converse property need not hold if there is only a
mean photon number constraint). Our first theorem demonstrates that Koenig and
Smith's upper bound on the classical capacity of the thermal bosonic channel is
a strong converse rate, and we prove this result by utilizing the structural
decomposition of a thermal channel into a pure-loss channel followed by an
amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s
upper bound on the classical capacity of a thermal bosonic channel corresponds
to a strong converse rate, and we prove this result by relating success
probability to rate, the effective dimension of the output space, and the
purity of the channel as measured by the Renyi collision entropy. Finally, we
use similar techniques to prove that similar previously known upper bounds on
the classical capacity of an additive noise bosonic channel correspond to
strong converse rates.Comment: Accepted for publication in Physical Review A; minor changes in the
text and few reference
Achieving the physical limits of the bounded-storage model
Secure two-party cryptography is possible if the adversary's quantum storage
device suffers imperfections. For example, security can be achieved if the
adversary can store strictly less then half of the qubits transmitted during
the protocol. This special case is known as the bounded-storage model, and it
has long been an open question whether security can still be achieved if the
adversary's storage were any larger. Here, we answer this question positively
and demonstrate a two-party protocol which is secure as long as the adversary
cannot store even a small fraction of the transmitted pulses. We also show that
security can be extended to a larger class of noisy quantum memories.Comment: 10 pages (revtex), 2 figures, v2: published version, minor change
Unconditional security from noisy quantum storage
We consider the implementation of two-party cryptographic primitives based on
the sole assumption that no large-scale reliable quantum storage is available
to the cheating party. We construct novel protocols for oblivious transfer and
bit commitment, and prove that realistic noise levels provide security even
against the most general attack. Such unconditional results were previously
only known in the so-called bounded-storage model which is a special case of
our setting. Our protocols can be implemented with present-day hardware used
for quantum key distribution. In particular, no quantum storage is required for
the honest parties.Comment: 25 pages (IEEE two column), 13 figures, v4: published version (to
appear in IEEE Transactions on Information Theory), including bit wise
min-entropy sampling. however, for experimental purposes block sampling can
be much more convenient, please see v3 arxiv version if needed. See
arXiv:0911.2302 for a companion paper addressing aspects of a practical
implementation using block samplin
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