One-time-pad encryption model for nonlocal correlations

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-signaling condition. As our design mimics the famous symmetric key encryption system called the 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 nonclassical 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.