Superluminal signaling with nonlocal boxes

Philip R. Wallace

Steven Weinstein

Sibasish Ghosh A

Govind Lal Sidhardh, Manik Banik

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.

V. Vilasini, Roger Colbeck

A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by considering various information-theoretic principles. Here, we initiate a similar approach considering relativistic causality principles. No superluminal causation (NSC) and no superluminal signaling (NSS) are distinct relativistic principles, requiring respectively that causal influence/the ability of agents to signal are within the future lightcone. After formalizing their distinction, we investigate how well theories constrained by NSC and NSS perform in a task that involves generating nonclassical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or postquantum) satisfying NSC. However, we show that theories violating NSC but satisfying NSS can perfectly achieve the task. We give a protocol that would, in a world allowing superluminal causation, enable its operational certification without violating NSS, in general spacetimes. In the case of (1 + 1)-dimensional Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of nonclassical postquantum resources: PR boxes and jamming. Our work offers insights into the role of different relativistic causality principles in fundamental physics and paves the way for characterizing the information-theoretic structure of theories obeying such principles.