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One-time Pad Encryption Model for Non-local Correlations

Govind Lal Sidhardh, Manik Banik

TL;DR

The paper introduces an OTP-box hidden-variable model to explain Bell-type nonlocal correlations under the operational no-signalling constraint by embedding instantaneous ontic signaling into a shared cryptographic key; randomness in the hidden-variable distribution ensures NS at the observed level, drawing a parallel to De Broglie-Bohm theory. It shows that extremal NS correlations like PR-boxes can be realized as OTP-boxes and extends this to broader NS vertices, including generalized and noisy variants, thereby providing a cryptographic interpretation of nonlocality and information-processing tasks. The work connects nonlocality to cryptographic concepts such as one-time pads and homomorphic encryption, recasting the Van Dam protocol and analyzing Information Causality to delineate between post-quantum and quantum-like correlations. Overall, the OTP framework yields intuitive mechanisms for the collapse of communication complexity, offers a path to model quantum correlations via controlled noise or limited ontic signaling, and invites further cross-pollination between cryptography and foundational studies of nonlocality.

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.

One-time Pad Encryption Model for Non-local Correlations

TL;DR

The paper introduces an OTP-box hidden-variable model to explain Bell-type nonlocal correlations under the operational no-signalling constraint by embedding instantaneous ontic signaling into a shared cryptographic key; randomness in the hidden-variable distribution ensures NS at the observed level, drawing a parallel to De Broglie-Bohm theory. It shows that extremal NS correlations like PR-boxes can be realized as OTP-boxes and extends this to broader NS vertices, including generalized and noisy variants, thereby providing a cryptographic interpretation of nonlocality and information-processing tasks. The work connects nonlocality to cryptographic concepts such as one-time pads and homomorphic encryption, recasting the Van Dam protocol and analyzing Information Causality to delineate between post-quantum and quantum-like correlations. Overall, the OTP framework yields intuitive mechanisms for the collapse of communication complexity, offers a path to model quantum correlations via controlled noise or limited ontic signaling, and invites further cross-pollination between cryptography and foundational studies of nonlocality.

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.
Paper Structure (12 sections, 5 theorems, 18 equations, 1 figure)

This paper contains 12 sections, 5 theorems, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries and set-up
  3. Bipartite no-signaling correlations
  4. De Broglie-Bohm theory
  5. OTP-box
  6. OTP model for nonlocal correlations
  7. OTP Model: Implications
  8. Collapse of communication complexity
  9. Van Dam protocol
  10. The principle of Information Causality
  11. Discussions
  12. IC and N-OTP model

Key Result

Lemma 1

The input-output correlation obtained from an OTP-box satisfies NS if and only if the distribution of the hidden variable within the black box (the key) is uniform, i.e., $P(\lambda)=1/2$.

Figures (1)

  • Figure 1: An illustration of the OTP box. Given inputs $x$ and $y$ to Alice and Bob, respectively, the box outputs the encrypted form of $f(x,y)$ at Bob's end and the associated key at Alice's end. In OTP encryption, the key is drawn uniformly randomly to comply with the operational NS condition.

Theorems & Definitions (13)

  • Definition 1
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Definition 2
  • Theorem 2
  • proof
  • Definition 3
  • Theorem 3
  • ...and 3 more