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