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arXiv:2303.17268 · Quantum

Classical-to-quantum non-signalling boxes

Carolina Moreira Ferrera, Robin Simmons, James Purcell, Daniel Collins, Sandu Popescu

Published Aug 22, 2024• 0 citations
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Abstract

Here we introduce the concept of classical input – quantum output (C-Q) non-signalling boxes, a generalisation of the classical input – classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better understanding of the relation between quantum nonlocality and non-locality beyond quantum mechanics. The main issue discussed in the paper is whether there exist 'genuine' C-Q boxes or all C-Q boxes can be built from objects already known, namely C-C boxes acting on pre-shared entangled quantum particles. We show that large classes of C-Q boxes are non-genuine. In particular, we show that all bi-partite C-Q boxes with outputs that are pure states are non-genuine. We also present various strategies for addressing the general problem, i.e. for multi-partite C-Q boxes which output mixed states, whose answer is still open. Finally, we show that even some very simple non-genuine C-Q boxes require large amounts of C-C nonlocal correlations in order to simulate them.

DOI
10.22331/q-2024-08-22-1443

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Here we introduce the concept of classical input – quantum output (C-Q) non-signalling boxes, a generalisation of the classical input – classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better understanding of the relation between quantum nonlocality and non-locality beyond quantum mechanics. The main issue discussed in the paper is whether there exist 'genuine' C-Q boxes or all C-Q boxes can be built from objects already known, namely C-C boxes acting on pre-shared entangled quantum particles. We show that large classes of C-Q boxes are non-genuine. In particular, we show that all bi-partite C-Q boxes with outputs that are pure states are non-genuine. We also present various strategies for addressing the general problem, i.e. for multi-partite C-Q boxes which output mixed states, whose answer is still open. Finally, we show that even some very simple non-genuine C-Q boxes require large amounts of C-C nonlocal correlations in order to simulate them.
Genuine multpartite quantum nonlocality can be quantified by the communication cost needed to reproduce the nonlocal correlation by classical communication models. This prompts the question as to how one may provide such an operational characterization for the nonclassicality of local multipartite correlations arising from genuinely quantum states possessing quantum discord. To answer this question, we consider a classical simulation protocol where one of the parties pre-share a random variable with the other parties who may also share arbitrary randomness. We demonstrate that genuine nonclassicality of local multipartite correlations is necessary for implying genuine superlocality which is the requirement for a larger dimension of the random variable in the above classical simulation protocol than that of quantum state that can generate the nonclassical correlations.
By studying generalized non-signalling theories, the hope is to find out what makes quantum mechanics so special. In the present paper, we revisit the paradigmatic model of non-signalling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized non-signalling model featuring quantum-like dynamics. In particular, we present the coupler, a device enabling non-locality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.
One of the most fascinating consequences of quantum theory is non‐locality, i.e., the fact that the measurement outcomes of (spatially separated) parts of a system can have a correlation unexplainable by shared classical information. Note that at the same time, these correlations are non‐signaling and do not allow for message transmission. Popescu and Rohrlich have defined a non‐local box as a “basic building block of non‐locality” and initiated a systematic study of non‐local correlations and their applications. However, they left open the question of whether any non‐signaling correlation can be simulated by such non‐local boxes. We show that the answer is yes with respect to arbitrarily accurate approximations.
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.
We introduce a framework in which a variety of theories can be defined that share two features with quantum mechanics: the no-signalling principle for states, and the fact that the global state of a multi-partite system can be completely specified by correlations between local measurements on the individual subsystems. The aim is to investigate the relationships between the physical properties of these theories and the information processing possibilities that each one offers. One of these theories, which we call Generalised Non-Signalling Mechanics, includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as non-local machines or PR boxes. By investigating these correlations in the context of a theory with well-defined dynamics, we hope to make further progress with a question raised by Popescu and Rohrlich: why does quantum mechanics not allow these strongly non-local correlations? We show that the existence of strongly non-local correlations forces much of the dynamics in this theory to be, in a certain sense, trivial, with consequences for teleportation, cryptography and computation. We also investigate another theory, which we call Generalised Local Mechanics, since all states in this theory are local. This has its own consequences for cryptography and computation. Finally, we raise the question of what further axiom(s) could be added to our framework in order uniquely to identify quantum mechanics.
Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum nonlocality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the no-signaling and independence principle. For the case of boxes without inputs, connecting pairs of bipartite sources and producing binary outputs, we prove that the sources and boxes producing local random outputs and maximal two-box correlations, i.e., ${E}_{2}=\sqrt{2}\ensuremath{-}1, {E}_{2}^{o}=1$, are essentially unique.