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Scientific Reports

Implementing no-signaling correlations as a service

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

Published May 10, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-024-59492-8

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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.
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.
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.
Abstract Classical and quantum physics provide fundamentally different predictions about experiments with separate observers that do not communicate, a phenomenon known as quantum nonlocality. This insight is a key element of our present understanding of quantum physics, and also enables a number of information processing protocols with security beyond what is classically attainable. Relaxing the pivotal assumption of no communication leads to new insights into the nature quantum correlations, and may enable new applications where security can be established under less strict assumptions. Here, we study such relaxations where different forms of communication are allowed. We consider communication of inputs, outputs, and of a message between the parties. Using several measures, we study how much communication is required for classical models to reproduce quantum or general no-signalling correlations, as well as how quantum models can be augmented with classical communication to reproduce no-signalling correlations.
It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They cannot, however, be used for superluminal signaling. It is also known that it is possible to write down sets of ``superquantum'' correlations that are more nonlocal than is allowed by quantum mechanics, yet are still nonsignaling. Viewed as an information-theoretic resource, superquantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signaling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signaling polytope in the case that two observers each choose from two possible measurements with ddd outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.
We derive an inequality that is necessary and sufficient to show Einstein-Podolsky-Rosen (EPR) steering in a scenario employing only correlations between two arbitrary dichotomic measurements on each party. Thus the inequality is a complete steering analogy of the Clauser-Horne-Shimony-Holt (CHSH) inequality, a generalization of the result of Cavalcanti et al. [E. G. Cavalcanti, C. J. Foster, M. Fuwa, and H. M. Wiseman, JOSA B 32, A74 (2015)]. We show that violation of the inequality only requires measuring over equivalence classes of mutually unbiased measurements on the trusted party and that in fact assuming a general two-qubit system arbitrary pairs of distinct projective measurements at the trusted party are equally useful. Via this it is found that for a given state the maximum violation of our EPR-steering inequality is equal to that for the CHSH inequality, so all states that are EPR steerable with CHSH-type correlations are also Bell nonlocal.
In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with nonlocality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly. The authorization levels are encoded in the nonlocal resources distributed to the users and subsequently confirmed by their ability to win Clauser-Horne-Shimony-Holt games using such resources. We formalize the protocol, prove its security, and frame it in a device-independent setting employing the notion of Clauser-Horne-Shimony-Holt self-testing via simulation. Finally, we provide a proof-of-concept implementation using the Qiskit open-source framework.