252 research outputs found
"Pretty strong" converse for the private capacity of degraded quantum wiretap channels
In the vein of the recent "pretty strong" converse for the quantum and
private capacity of degradable quantum channels [Morgan/Winter, IEEE Trans.
Inf. Theory 60(1):317-333, 2014], we use the same techniques, in particular the
calculus of min-entropies, to show a pretty strong converse for the private
capacity of degraded classical-quantum-quantum (cqq-)wiretap channels, which
generalize Wyner's model of the degraded classical wiretap channel.
While the result is not completely tight, leaving some gap between the region
of error and privacy parameters for which the converse bound holds, and a
larger no-go region, it represents a further step towards an understanding of
strong converses of wiretap channels [cf. Hayashi/Tyagi/Watanabe,
arXiv:1410.0443 for the classical case].Comment: 5 pages, 1 figure, IEEEtran.cls. V2 final (conference) version,
accepted for ISIT 2016 (Barcelona, 10-15 July 2016
The strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory
Establishing the strong converse theorem for a communication channel confirms
that the capacity of that channel, that is, the maximum achievable rate of
reliable information communication, is the ultimate limit of communication over
that channel. Indeed, the strong converse theorem for a channel states that
coding at a rate above the capacity of the channel results in the convergence
of the error to its maximum value 1 and that there is no trade-off between
communication rate and decoding error. Here we prove that the strong converse
theorem holds for the product-state capacity of quantum channels with ergodic
Markovian correlated memory.Comment: 11 pages, single colum
Short proofs of the Quantum Substate Theorem
The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen (2002) gives
us a powerful operational interpretation of relative entropy, in fact, of the
observational divergence of two quantum states, a quantity that is related to
their relative entropy. Informally, the theorem states that if the
observational divergence between two quantum states rho, sigma is small, then
there is a quantum state rho' close to rho in trace distance, such that rho'
when scaled down by a small factor becomes a substate of sigma. We present new
proofs of this theorem. The resulting statement is optimal up to a constant
factor in its dependence on observational divergence. In addition, the proofs
are both conceptually simpler and significantly shorter than the earlier proof.Comment: 11 pages. Rewritten; included new references; presented the results
in terms of smooth relative min-entropy; stronger results; included converse
and proof using SDP dualit
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
Partial decode-forward for quantum relay channels
A relay channel is one in which a Source and Destination use an intermediate
Relay station in order to improve communication rates. We propose the study of
relay channels with classical inputs and quantum outputs and prove that a
"partial decode and forward" strategy is achievable. We divide the channel uses
into many blocks and build codes in a randomized, block-Markov manner within
each block. The Relay performs a standard Holevo-Schumacher-Westmoreland
quantum measurement on each block in order to decode part of the Source's
message and then forwards this partial message in the next block. The
Destination performs a novel "sliding-window" quantum measurement on two
adjacent blocks in order to decode the Source's message. This strategy achieves
non-trivial rates for classical communication over a quantum relay channel.Comment: 7 pages, submission to the 2012 International Symposium on
Information Theory (ISIT 2012), Boston, MA, US
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