Quantum Nonlocality and Device-Independent Randomness are Robust to Noisy Signaling Channels

TL;DR

This paper demonstrates that quantum nonlocality and device-independent randomness remain robust even when noisy signaling channels are present, by characterizing local polytopes and Bell inequalities under such conditions.

Contribution

It provides a complete characterization of local polytopes and Bell inequalities in scenarios with noisy signaling channels, extending the robustness of quantum nonlocality.

Findings

Bell inequalities certifying non-signaling quantum correlations identified

Robustness of DI randomness exceeds that of CHSH under depolarizing noise

Local polytope characterized for scenarios with noisy inputs

Abstract

Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a classical explanation can be ruled out if the devices perform certain measurements on an entangled quantum state, underpinning the security of cryptographic protocols that are device-independent (DI). For certain protocols, such as those performed in a tight space, it might be difficult to perfectly enforce the non-signaling assumption required in Bell's theorem. This prompts the question: is quantum nonlocality robust to such imperfections? We show that if a binary channel sends a noisy copy of one party's input to the other before any measurements take place, the answer is yes. We completely characterize the vertices and facets of the local polytope in this scenario, and identify Bell inequalities that certify non-signaling quantum correlations. This is possible even when a near perfect copy of the input is sent. We go on to show that the identified inequalities are more robust to depolarizing noise than the Clauser-Horne-Shimony-Holt inequality when certifying DI randomness in this scenario. In addition, we characterize the local polytope when both parties receive a noisy copy of each other's input and make similar conclusions, leaving many new potential Bell inequalities to be explored.