EPR Steering inequalities with Communication Assistance

TL;DR

This paper explores the classical communication needed to simulate EPR steering correlations, revealing that certain quantum states require infinite communication, while others can be simulated with limited bits, impacting our understanding of quantum nonlocality.

Contribution

It characterizes the set of bipartite states simulatable with limited classical communication and shows the necessity of infinite communication for maximally entangled states.

Findings

One bit of communication intersects with local hidden state models.

Infinite communication is needed to simulate maximally entangled states.

Two bits of communication could be experimentally falsified.

Abstract

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with $c$ bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information ($c=1$), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.