Quantum nonlocality from the probabilistic viewpoint

Weixiao Sun, Zhaohui Wei

Suppose two quantum circuit chips are located at different places, for which we do not have any prior knowledge, and cannot see the internal structures either. If we want to find out whether they have the same functions or not with certainty, what should we do? In this paper, we show that this realistic problem can be solved from the viewpoints of quantum nonlocality. Specifically, we design an elegant protocol that examines underlying quantum nonlocality. We prove that in the protocol the strongest nonlocality can be observed if and only if two quantum circuits are equivalent to each other. We show that the protocol also works approximately, where the distance between two quantum circuits can be lower and upper bounded analytically by observed quantum nonlocality. Furthermore, we also discuss the possibility to generalize the protocol to multipartite cases, i.e., if we do equivalence checking for multiple quantum circuits, we try to solve the problem in one go. Our work introduces a nontrivial application of quantum nonlocality in quantum engineering.

Mary Bell, Shan Gao

Sandu Popescu

Francesco Buscemi

Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, here we study the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled quantum state. An example illustrating this fact is provided.

Mustafa Mert Özyılmaz, Ruchi Thareja, Houssam Nasser

Nonlocal games provide a unified framework for studying the distinction between classical, quantum, and more general no-signaling correlations. In this work, we develop this perspective by connecting the Bell-locality framework to several complementary mathematical representations of nonlocal games and quantum strategies. We begin with local hidden-variable models, the CHSH inequality, and the role of Bell nonlocality as a device-independent witness of entanglement, and then introduce nonlocal games through the standard predicate/verifier formalism. We next examine a set of representative examples, including XOR games, the GHZ game, graph-based coloring games, the Mermin-Peres magic square game, and Hardy's paradox as a related logical manifestation of nonlocality. Building on this foundation, we compare four closely related representation frameworks: conditional-probability and correlation descriptions, Bell-functional formulations, entangled-value optimization, and the quantum-operator approach together with the Navascues-Pironio-Acin (NPA) hierarchy. These viewpoints are then instantiated for the CHSH, magic square, and GHZ games, showing how each representation emphasizes a different aspect of the same underlying task. Taken together, these examples show that nonlocal games can be studied simultaneously as geometric objects in correlation space, optimization problems over entangled resources, and operator-theoretic constructions. This multi-representation viewpoint clarifies the relation between Bell inequality violations, perfect quantum strategies, pseudo-telepathy, and semidefinite relaxations of quantum correlations.

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