4.6 Article

Contextuality in Entanglement-assisted One-shot Classical Communication

Journal

QUANTUM
Volume 6, Issue -, Pages -

Publisher

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
DOI: 10.22331/q-2022-10-11-839

Keywords

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Funding

  1. Richardson Endowment in the Department of Physics, Duke University
  2. Melvin J. Rieger Scholarship Fund in Physics and Robert E. Boyer Endowed Presidential Scholarship for Natural Sciences in the Department of Physics, University of Texas at Austin
  3. Charge de Recherche fellowship of the Fonds de la Recherche Scientifique -FNRS (F.R.S.-FNRS), Belgium
  4. Perimeter Institute for Theoretical Physics
  5. Government of Canada through the Department of Innovation, Science and Economic Development Canada
  6. Province of Ontario through the Ministry of Research, Innovation and Science

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This paper investigates the entanglement-assisted one-shot classical communication problem. It shows that entanglement can increase the one-shot zero-error capacity in the zero-error regime but not in the presence of noise or measurements. By examining the one-shot success probability of sending a fixed number of classical messages, the paper demonstrates that preparation contextuality can enhance the success probability. Additionally, a mapping between this communication task and a corresponding nonlocal game is established.
We consider the problem of entanglement-assisted one-shot classical communication. In the zero-error regime, entanglement can increase the one-shot zero-error capacity of a family of classical channels following the strategy of Cubitt et al., Phys. Rev. Lett. 104, 230503 (2010). This strategy uses the Kochen-Specker theorem which is applicable only to projective measurements. As such, in the regime of noisy states and/or measurements, this strategy cannot increase the capacity. To accommodate generically noisy situations, we examine the one-shot success probability of sending a fixed number of classical messages. We show that preparation contextuality powers the quantum advantage in this task, increasing the one-shot success probability beyond its classical maximum. Our treatment extends beyond Cubitt et al. and includes, for example, the experimentally implemented protocol of Prevedel et al., Phys. Rev. Lett. 106, 110505 (2011). We then show a mapping between this communication task and a corresponding nonlocal game. This mapping generalizes the connection with pseudotelepathy games previously noted in the zero-error case. Finally, after motivating a constraint we term context-independent guessing, we show that contextuality witnessed by noise-robust noncontextuality inequalities obtained in R. Kunjwal, Quantum 4, 219 (2020), is sufficient for enhancing the one-shot success probability. This provides an operational meaning to these inequalities and the associated hypergraph invariant, the weighted max-predictability, introduced in R. Kunjwal, Quantum 3, 184 (2019). Our results show that the task of entanglement-assisted one-shot classical communication provides a fertile playground to study the interplay of the Kochen-Specker theorem, Spekkens contextuality, and Bell nonlocality.

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