Contextuality in entanglement-assisted one-shot classical communication
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We consider the problem of entanglement-assisted one-shot classical communication. In the zero-error regime, entanglement can enhance 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 makes crucial use of the Kochen-Specker theorem which is applicable only to projective measurements. In the generic regime of noisy entangled states and/or noisy local measurements, the one-shot zero-error capacity cannot be increased using this strategy. We therefore study the enhancement of the one-shot success probability of sending a fixed number of messages across a classical channel. We obtain three main results. Firstly, we show that preparation contextuality powers the quantum advantage in this task, enhancing the one-shot success probability beyond its classical maximum. Our treatment is general, extending beyond the scenarios in Cubitt et al., e.g., the experimentally implemented protocol of Prevedel et al., Phys. Rev. Lett. 106, 110505 (2011). Secondly, we show a mapping between this one-shot classical communication task and a corresponding nonlocal game, demonstrating a subtle interplay between preparation contextuality and Bell nonlocality. 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 in the communication task, 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. The hypergraph invariant – weighted max-predictability – introduced in R. Kunjwal, Quantum 3, 184 (2019), thus finds an application in certifying a quantum advantage in this task.
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