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arXiv:2212.06769

Simulating nonlocal no-signaling boxes

Mátyás Koniorczyk, Péter Naszvadi, András Bodor, O. Hanyecz, Петер Адам, Miklós Pintér

Published Dec 13, 2022• 0 citations
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Abstract

We present a computer framework to simulate two-party boxes that exhibit nonclassical no-signaling correlations through a Web-based application programming interface (RESTful Web API). Unlike real quantum-based correlations, the simulated ones are not instantaneous and are created via communication with a trusted server. They can, however, be useful in a number of applications, including e.g. teaching the use of nonlocal correlations, designing and testing infocommunication systems, and engineering software interfaces for new quantum hardware. We demonstrate the use of the API via the simple implementation of the Clauser-Horne-Shimony-Holt game. Up to our knowledge no such a framework has been implemented or proposed thus far.

DOI
10.48550/arxiv.2212.06769

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We present a computer framework to simulate two-party boxes that exhibit nonclassical no-signaling correlations through a Web-based application programming interface (RESTful Web API). Unlike real quantum-based correlations, the simulated ones are not instantaneous and are created via communication with a trusted server. They can, however, be useful in a number of applications, including e.g. teaching the use of nonlocal correlations, designing and testing infocommunication systems, and engineering software interfaces for new quantum hardware. We demonstrate the use of the API via the simple implementation of the Clauser-Horne-Shimony-Holt game. Up to our knowledge no such a framework has been implemented or proposed thus far.
We deal with no-signaling correlations that include Bell-type quantum nonlocality. We consider a logical implementation using a trusted central server with encrypted connections to clients. We show that in this way it is possible to implement two-party no-signaling correlations in an asynchronous manner. While from the point of view of physics our approach can be considered as the computer emulation of the results of measurements on entangled particles, from the software engineering point of view it introduces a primitive in communication protocols that can be capable of coordinating agents without revealing the details of their actions. We present an actual implementation in the form of a Web-based application programming interface (RESTful Web API). We demonstrate the use of the API via the simple implementation of the Clauser-Horne-Shimony-Holt game.
Bell nonlocality exemplifies the most profound departure of quantum theory from classical realism. Yet, the extent of nonlocality in quantum theory is intrinsically bounded, falling short of the correlations permitted by the relativistic causality (the no-signaling) principle. A paradigmatic example is the Popescu-Rohrlich correlation: two distant parties sharing arbitrary entanglement cannot achieve this correlation, though it can be simulated with classical communication between them. Here we show how such post-quantum correlations can instead be simulated using intrinsically non-signaling physical resources, and implement the proposed scheme using a quantum circuit on a four-qubit photonic platform. Unlike the conventional approaches, our method exploits dynamical correlations between distinct physical systems, with intrinsic randomness suppressing any signaling capacity. This enables the realization of post-quantum correlations both with and without entanglement. We also analyze how the simulation scheme extends to beyond quantum nonlocal correlations in multipartite systems. Our experimental demonstration using a photonic system establishes a versatile framework for exploring post-quantum correlations in both foundational settings and as a resource for computation and security applications.
Abstract We define a family of ‘no signaling ’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining corre-lations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The mar-ginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no signaling ’ poly-tope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum re-sources for all inputs. We comment on the significance of these results for contextu-ality and nonlocality in ‘no signaling ’ theories.
The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell's correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction [Formula: see text] of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.
We address the question of when quantum entanglement is a useful resource for information processing tasks by presenting a new class of nonlocal games that are simple, direct, generalizations of the Clauser Horne Shimony Holt game. For some ranges of the parameters that specify the games, quantum mechanics offers an advantage, while, surprisingly, for others quantum mechanics is no more powerful than classical mechanics in performing the nonlocal task. This sheds new light on the difference between classical, quantum and super-quantum 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.