Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects

TL;DR

This paper explores simulating quantum entanglement using classical communication and nonlocal effects, extending Toner and Bacon's protocol to show how measurement outcomes can be deduced or influenced instantaneously.

Contribution

It introduces a nonlocal variant of Toner and Bacon's protocol replacing classical communication with nonlocal effects, and applies the approach to Svozil's protocol.

Findings

Bob can deduce Alice's measurement outputs with minimal information

Nonlocal effects can replace classical communication in simulating entanglement

Protocols can be extended to other quantum correlation models

Abstract

Bell's theorem states that quantum mechanics is not a locally causal theory. This state is often interpreted as nonlocality in quantum mechanics. Toner and Bacon [Phys. Rev. Lett. \textbf{91}, 187904 (2003)] have shown that a shared random-variables theory augmented by one bit of classical communication exactly simulates the Bell correlation in a singlet state. In this paper, we show that in Toner and Bacon protocol, one of the parties (Bob) can deduce another party's (Alice) measurement outputs, if she only informs Bob of one of her own outputs. Afterwards, we suggest a nonlocal version of Toner and Bacon protocol wherein classical communications is replaced by nonlocal effects, so that Alice's measurements cause instantaneous effects on Bob's outputs. In the nonlocal version of Toner and Bacon's protocol, we get the same result again. We also demonstrate that the same approach is applicable to Svozil's protocol.