559 research outputs found

### Strong Secrecy for Multiple Access Channels

We show strongly secret achievable rate regions for two different wiretap
multiple-access channel coding problems. In the first problem, each encoder has
a private message and both together have a common message to transmit. The
encoders have entropy-limited access to common randomness. If no common
randomness is available, then the achievable region derived here does not allow
for the secret transmission of a common message. The second coding problem
assumes that the encoders do not have a common message nor access to common
randomness. However, they may have a conferencing link over which they may
iteratively exchange rate-limited information. This can be used to form a
common message and common randomness to reduce the second coding problem to the
first one. We give the example of a channel where the achievable region equals
zero without conferencing or common randomness and where conferencing
establishes the possibility of secret message transmission. Both coding
problems describe practically relevant networks which need to be secured
against eavesdropping attacks.Comment: 55 page

### Strong Converse for Identification via Quantum Channels

In this paper we present a simple proof of the strong converse for
identification via discrete memoryless quantum channels, based on a novel
covering lemma. The new method is a generalization to quantum communication
channels of Ahlswede's recently discovered appoach to classical channels. It
involves a development of explicit large deviation estimates to the case of
random variables taking values in selfadjoint operators on a Hilbert space.
This theory is presented separately in an appendix, and we illustrate it by
showing its application to quantum generalizations of classical hypergraph
covering problems.Comment: 11 pages, LaTeX2e, requires IEEEtran2e.cls. Some errors and omissions
corrected, references update

### 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

### 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

### 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

### A systematic study of non-ideal contacts in integer quantum Hall systems

In the present article we investigate the influence of the contact region on
the distribution of the chemical potential in integer quantum Hall samples, as
well as the longitudinal and Hall resistance as a function of the magnetic
field. First we use a standard quantum Hall sample geometry and analyse the
influence of the length of the leads where current enters/leaves the sample and
the ratio of the contact width to the width of these leads. Furthermore we
investigate potential barriers in the current injecting leads and the
measurement arms in order to simulate non-ideal contacts. Second we simulate
nonlocal quantum Hall samples with applied gating voltage at the metallic
contacts. For such samples it has been found experimentally that both the
longitudinal and Hall resistance as a function of the magnetic field can change
significantly. Using the nonequilibrium network model we are able to reproduce
most qualitative features of the experiments.Comment: 29 pages, 16 Figure

### Screening Model of Magnetotransport Hysteresis Observed in Bilayer Quantum Hall Systems

We report on theoretical and experimental investigations of a novel
hysteresis effect that has been observed on the magnetoresistance of
quantum-Hall bilayer systems. Extending to these system a recent approach,
based on the Thomas-Fermi-Poisson nonlinear screening theory and a local
conductivity model, we are able to explain the hysteresis as being due to
screening effects such as the formation of ``incompressible strips'', which
hinder the electron density in a layer within the quantum Hall regime to reach
its equilibrium distribution.Comment: 9 pages, 4 figures, to appear in Physica

### On Fast and Robust Information Spreading in the Vertex-Congest Model

This paper initiates the study of the impact of failures on the fundamental
problem of \emph{information spreading} in the Vertex-Congest model, in which
in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message
to all of its neighbors.
Our contribution to coping with failures is twofold. First, we prove that the
randomized algorithm which chooses uniformly at random the next message to
forward is slow, requiring $\Omega(n/\sqrt{k})$ rounds on some graphs, which we
denote by $G_{n,k}$, where $k$ is the vertex-connectivity.
Second, we design a randomized algorithm that makes dynamic message choices,
with probabilities that change over the execution. We prove that for $G_{n,k}$
it requires only a near-optimal number of $O(n\log^3{n}/k)$ rounds, despite a
rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing
probabilities that change according to the execution is of independent
interest.Comment: Appears in SIROCCO 2015 conferenc

### On q-ary codes correcting all unidirectional errors of a limited magnitude

We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of
unidirectional errors of level l. That is, the transmission channel is such
that the received word cannot contain both a component larger than the
transmitted one and a component smaller than the transmitted one. Moreover, the
absolute value of the difference between a transmitted component and its
received version is at most l.
We introduce and study q-ary codes capable of correcting all unidirectional
errors of level l. Lower and upper bounds for the maximal size of those codes
are presented.
We also study codes for this aim that are defined by a single equation on the
codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting
binary asymmetric errors). We finally consider the problem of detecting all
unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian
Academy of Sciences, special issue dedicated to Rom Varshamo

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