7 research outputs found
Secrecy Results for Compound Wiretap Channels
We derive a lower bound on the secrecy capacity of the compound wiretap
channel with channel state information at the transmitter which matches the
general upper bound on the secrecy capacity of general compound wiretap
channels given by Liang et al. and thus establishing a full coding theorem in
this case. We achieve this with a stronger secrecy criterion and the maximum
error probability criterion, and with a decoder that is robust against the
effect of randomisation in the encoding. This relieves us from the need of
decoding the randomisation parameter which is in general not possible within
this model. Moreover we prove a lower bound on the secrecy capacity of the
compound wiretap channel without channel state information and derive a
multi-letter expression for the capacity in this communication scenario.Comment: 25 pages, 1 figure. Accepted for publication in the journal "Problems
of Information Transmission". Some of the results were presented at the ITW
2011 Paraty [arXiv:1103.0135] and published in the conference paper available
at the IEEE Xplor
Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels
We investigate entanglement transmission over an unknown channel in the
presence of a third party (called the adversary), which is enabled to choose
the channel from a given set of memoryless but non-stationary channels without
informing the legitimate sender and receiver about the particular choice that
he made. This channel model is called arbitrarily varying quantum channel
(AVQC). We derive a quantum version of Ahlswede's dichotomy for classical
arbitrarily varying channels. This includes a regularized formula for the
common randomness-assisted capacity for entanglement transmission of an AVQC.
Quite surprisingly and in contrast to the classical analog of the problem
involving the maximal and average error probability, we find that the capacity
for entanglement transmission of an AVQC always equals its strong subspace
transmission capacity. These results are accompanied by different notions of
symmetrizability (zero-capacity conditions) as well as by conditions for an
AVQC to have a capacity described by a single-letter formula. In he final part
of the paper the capacity of the erasure-AVQC is computed and some light shed
on the connection between AVQCs and zero-error capacities. Additionally, we
show by entirely elementary and operational arguments motivated by the theory
of AVQCs that the quantum, classical, and entanglement-assisted zero-error
capacities of quantum channels are generically zero and are discontinuous at
every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2
and arXiv:1010.0418. Published "Online First" in Communications in
Mathematical Physics, 201
Coding Theorem for a Class of Quantum Channels with Long-Term Memory
In this paper we consider the transmission of classical information through a
class of quantum channels with long-term memory, which are given by convex
combinations of product channels. Hence, the memory of such channels is given
by a Markov chain which is aperiodic but not irreducible. We prove the coding
theorem and weak converse for this class of channels. The main techniques that
we employ, are a quantum version of Feinstein's Fundamental Lemma and a
generalization of Helstrom's Theorem.Comment: Some typos correcte