Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

Abstract

In this paper we propose a new model for arbitrarily varying classical-quantum channels. In this model a jammer has side information. We consider two scenarios. In the first scenario the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. We determine the capacity for both average and maximum error criteria for both scenarios. We also establish the strong converse. We show that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity.

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

“…A deterministic capacity formula for this is still unknown. In particular, [13] shows a violation of Ahlswede dichotomy in our scenario.…”

“…Most of the previous works in AVCQCs consider the case when the jammer knows the coding scheme, but has no side information about the codeword of the transmitters. However for secure communications this assumption may be too optimistic, since [13] shows that the jammer really can archive a better jamming strategy when he knows the codeword. Thus we concentrate on message transmission over classical quantum channels with a jammer with additional side information about the codeword.…”

“…Due to the non-commutativity of quantum operators, many techniques, concepts and methods of classical information theory, for instance, non-standard decoder and list decoding (which has been used in [25]'s proof), may not be extended to quantum information theory. In [13] we determined the random assisted capacities of AVCQCs when the jammer has access to the channel input.…”

“…This work is a extension of our previous paper [13], where we determined the randomness assisted capacity of AVCQCs with a jammer knowing the channel input. However, as [18] showed, common randomness is a very "costly" resource.…”

“…In many applications, especially for secure communications, it is too optimistic to assume this. In [13] it has been show that the jammer can benefice from his knowledge about the sending codeword, i.e, he may have a better jamming strategy. Thus in our previous paper [13] we considered the scenario when the jammer knows both the coding scheme and the input codeword.…”