One-time Pad Encryption Model for Non-local Correlations

TL;DR

This paper introduces a cryptographic-inspired model for Bell nonlocal correlations using a one-time pad analogy, providing new insights into nonlocal boxes, communication complexity, and quantum correlations.

Contribution

It proposes a novel OTP-based framework for nonlocal boxes, connecting cryptography principles with quantum nonlocality and analyzing protocols like Van Dam's within this context.

Findings

The OTP model clarifies the breakdown of communication complexity with nonlocal boxes.

Connections between Van Dam protocol and homomorphic encryption are established.

Information Causality constrains hidden variable models of nonlocal correlations.

Abstract

We present a cryptographic-inspired framework for modeling Bell nonlocal correlations. Drawing inspiration from the renowned De Broglie-Bohm theory, we conceptualize nonlocal boxes as realistic systems featuring instantaneous signaling at the hidden variable level. By introducing randomness into the distribution of the hidden variable the superluminal signaling model is made compatible with the operational no-signalling condition. As our design mimics the famous symmetric key encryption system called {\it One-time Pad} (OTP), we call this the OTP model for nonlocal boxes. We illustrate the efficacy of this model through various esoteric examples related to the non-classical nature of nonlocal boxes. In particular, the breakdown of communication complexity using nonlocal boxes can be better understood in this framework. Additionally, we delve into the Van Dam protocol, revealing its connection to homomorphic encryption studied in cryptography. Exploring potential avenues for encapsulating quantum-realizable nonlocal correlations within our framework, we highlight that the Information Causality principle imposes additional constraints at the hidden variable level. Present work thus orchestrates the results in classical cryptography to improve our understanding of nonlocal correlations and welcomes further research to this connection.