Duan, R;
Severini, S;
Winter, A;
(2016)
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback.
IEEE Transactions On Information Theory
, 62
(9)
pp. 5260-5277.
10.1109/TIT.2016.2562580.
Preview |
Text
1502.02987v3.pdf - Accepted Version Download (569kB) | Preview |
Abstract
We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions.
| Type: | Article |
|---|---|
| Title: | On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIT.2016.2562580 |
| Publisher version: | http://doi.org/10.1109/TIT.2016.2562580 |
| Language: | English |
| Additional information: | Copyright © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. |
| Keywords: | Science & Technology, Technology, Computer Science, Information Systems, Engineering, Electrical & Electronic, Computer Science, Engineering, Quantum Information, Zero-error Capacity, Feedback, Entanglement-assisted Capacity, Reverse Shannon Theorem, Classical Capacity, States |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1488046 |
Archive Staff Only
 |
View Item |
