Contextuality in entanglement-assisted one-shot classical communication

This seminar will be followed by coffee and biscuits in the DB crush area.

Abstract

The fact that quantum theory allows the possibility of quantum advantage over classical resources is powered by its nonclassicality. This nonclassicality can take many forms, e.g., entanglement, incompatibility, contextuality, Bell nonlocality, etc. By studying the task of entanglement-assisted one-shot classical communication, we consider the interplay of three notions of nonclassicality: 1) Kochen-Specker contextuality, 2) Spekkens contextuality, and 3) Bell nonlocality. Specifically, we study the following communication problem: Alice (the sender) is connected to Bob (the receiver) via a noisy classical channel. They are allowed access to shared entanglement and can implement local quantum measurements. It is known that for a certain family of classical channels inspired by the Kochen-Specker theorem, the number of messages that can be sent without error over the classical channel (i.e., it one-shot zero-error capacity) can be increased with access to shared entanglement. This zero-error result due to Cubitt et al. [Phys. Rev. Lett. 104, 230503 (2010)] is also intimately related to nonlocal games that admit perfect quantum winning strategies. We study this communication problem in the noisy regime where the Kochen-Specker theorem is inapplicable. In doing so, we show the intimate connection of this problem with noise-robust contextuality in the formulation proposed by Spekkens [Phys. Rev. A 71, 052108 (2005)] and with a family of nonlocal games inspired by the communication problem. Under an assumption that the parties do not trust the probabilities associated with the classical channel, but trust only its possibilistic structure, we also show that noise-robust contextuality witnessed by a hypergraph invariant is sufficient for quantum advantage in this task. This provides an operational meaning to the contextuality witnesses obtained in R. Kunjwal, Quantum 4, 219 (2020).