Arbitrarily small amounts of correlation for arbitrarily varying quantum channels

2019 IEEE International Symposium on Information Theory (ISIT)

Cai

2019

Self Cite

In this paper we analyze the capacity of a general model for arbitrarily varying classical-quantum channels when the sender and the receiver use a weak resource. In this model a jammer has side information about the channel input.We determine the correlation assisted capacity of AVCQCs with a jammer knowing the channel input. We deliver a single letter formula for the correlation assisted capacity. This formula as a function of the channel parameters is

Section: Fig 4 Avcqc When the Jammer Knows The Coding Scheme Havingmentioning

confidence: 99%

Message Transmission over Classical Quantum Channels with a Jammer with Side Information, Correlation as Resource and Common Randomness Generating

2019 IEEE International Symposium on Information Theory (ISIT)

Cai

2019

Self Cite

“…After we indicated why the super-activation protocol works we do now want to switch the topic and highlight a few connections to related problems and technical difficulties: It is evident from the existing literature on AVCs [5], arbitrarily varying classical-quantum channels [14] and on the quantification of shared randomness [7,28,31,41,39] that the latter is not an easy task. A brief overview concerning the connections between quantification of shared randomness and arbitrarily varying channels has been given in [14].…”

Section: Models and Operational Definitionsmentioning

confidence: 99%

“…A brief overview concerning the connections between quantification of shared randomness and arbitrarily varying channels has been given in [14]. Our focus here is on systems that use only common randomness in various different ways.…”

Section: Models and Operational Definitionsmentioning

confidence: 99%

The arbitrarily varying wiretap channel - secret randomness, stability and super-activation

Nötzel

Wiese

2015 IEEE International Symposium on Information Theory (ISIT)

2015

We define the common randomness assisted capacity of an arbitrarily varying channel (AVWC) when the Eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available, and derive the capacity. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of "wasting" a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this work we provide further insight into this phenomenon by providing a class of codes that is capacity-achieving and does not convey any information to the Eavesdropper.

“…In [23], a classification of various resources is given. A distinction is made between two extremal cases: randomness and correlation.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, correlation is the weakest resource. The work [23] also puts emphasis on the quantification of the differences between correlation and common randomness and used the arbitrarily varying classical-quantum channel as a method of proof. It can be shown that common randomness is a stronger resource than correlation in the following sense: An example is given where not even a finite amount of common randomness can be extracted from a given correlation.…”

Section: Introductionmentioning

confidence: 99%

Classical-quantum arbitrarily varying wiretap channel: common randomness assisted code and continuity

Cai

Deppe

et al. 2016

Quantum Inf Process

Self Cite

We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels. Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legitimate receiver and varies arbitrarily from the sender to the eavesdropper. We examine when the secrecy capacity is a continuous function of the system parameters as an application and show that resources, e.g., having access to a perfect copy of the outcome of a random experiment, can guarantee continuity of the capacity function of arbitrarily varying classical-quantum wiretap channels.