Zero-error channel capacity and simulation assisted by non-local correlations

Toby S. Cubitt, Debbie Leung, William Matthews, Andreas Winter

Research output: Contribution to journalReview articlepeer-review

49 Scopus citations

Abstract

The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i.e., shared randomness, shared entanglement and arbitrary nonsignalling correlations. When the channel being simulated is noiseless, this is zero-error coding assisted by correlations. When the resource channel is noiseless, it is the reverse problem of simulating a noisy channel exactly by a noiseless one, assisted by correlations. In both cases, separations between the power of the different classes of assisting correlations are exhibited for finite block lengths. The most striking result here is that entanglement can assist in zero-error communication. In the large block length limit, shared randomness is shown to be just as powerful as arbitrary nonsignalling correlations for exact simulation, but not for asymptotic zero-error coding. For assistance by arbitrary nonsignalling correlations, linear programming formulas for the asymptotic capacity and simulation rates are derived, the former being equal (for channels with nonzero unassisted capacity) to the feedback-assisted zero-error capacity derived by Shannon. Finally, a kind of reversibility between nonsignalling-assisted zero-error capacity and exact simulation is observed, mirroring the usual reverse Shannon theorem.

Original languageEnglish
Article number5961832
Pages (from-to)5509-5523
Number of pages15
JournalIEEE Transactions on Information Theory
Volume57
Issue number8
DOIs
StatePublished - Aug 2011
Externally publishedYes

Keywords

  • Channel coding
  • graph capacities
  • quantum entanglement
  • zero-error information theory

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