N. Aharon, S. Machnes, B. Reznik, J. Silman, L. Vaidman
We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.
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Several variants of nonlocal games have been considered in the study of quantum entanglement and nonlocality. This paper concerns two of these variants, called quantum-classical games and extended nonlocal games. We give a construction of an extended nonlocal game from any quantum-classical game that allows one to translate certain facts concerning quantum- classical games to extended nonlocal games. In particular, based on work of Regev and Vidick, we conclude that there exist extended nonlocal games for which no finite-dimensional entangled strategy can be optimal. While this conclusion is a…
Bell nonlocality does not imply violation of nonlocal games
本文证明非局域博弈（确定性谓词）不能完整见证贝尔非局域性，存在量子可实现的非局域行为不违反任何此类博弈，且该现象在$X,Y\geq2$、$A,B\geq4$的二分场景中普遍存在。
We study a generalization of nonlocal games---which we call extended nonlocal games---in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski, and Wehner, which they also generalize. We prove that a natur…
We investigate the relation between Bell inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bell inequality, the converse is not true. As an illustration of the method we present a number of nonlocal games that admit better odds when played using quantum resources
Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations. In particular, we characterize when morphisms in these categories are monic, epic, sections, or retractions.
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.
Nonlocal game as a novel witness of the nonlocality of entanglement is of fundamental importance in various fields. The known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We first propose an efficient method to construct numerous multipartite games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providin…
A Nonlocality Anomaly and Extended Semiquantum Games
提出了通过扩展半量子博弈引入经典通信来消除部分纠缠态在非定域性异常的方法，并给出了异常发生的必要条件。
Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they differ. Advantage of nonlocal correlation has been demonstrated over fair strategies. In this work we s…
In this work we show how a vector-valued version of Schechtman's empirical method can be used to reduce the number of inputs in a nonlocal game $G$ while preserving the quotient $β^*(G)/β(G)$ of the quantum over the classical bias. We apply our method to the Khot-Vishnoi game, with exponentially many questions per player, to produce another game with polynomially many ($N\approx n^8$) questions so that the quantum over the classical bias is $Ω(n/\log^2 n)$.
Nonlocal Games as Cross-Platform Quantum Benchmarks: Exceeding unconditional classical bounds on trapped-ion processors
研究通过在四个囚禁离子量子处理器上实现14顶点图着色游戏，首次在非本地游戏中超越经典界限，展示了非本地游戏作为跨架构量子基准的潜力。
Nonlocal Games Revisited: A Representation-Theoretic Path from Bell Locality to Quantum Pseudo-Telepathy
本文通过连接贝尔局域性框架与非局域游戏的多种数学表示，探讨了非局域游戏作为几何对象、优化问题和算子构造的多维视角，揭示了贝尔不等式违反、完美量子策略与半正定松弛之间的关系。
We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e. no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria…
Decidability of fully quantum nonlocal games with noisy maximally entangled states
针对共享含噪最大纠缠态的完全量子非局部博弈，本文证明逼近其量子值可判定，并通过超算子 Fourier 分析给出所需态份数的可计算上界。
Application-level Benchmarking of Quantum Computers using Nonlocal Game Strategies
提出一种变分量子算法，通过将非定域博弈规则编码为哈密顿量来计算量子策略，并在14个量子硬件平台上评估图着色博弈策略以实现应用级基准测试。
Nonlocal games are extensions of Bell inequalities, aimed at demonstrating quantum advantage. These games are well suited for noisy quantum computers because they only require the preparation of a shallow circuit, followed by the measurement of non-commuting observable. Here, we consider the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018). We test this game by preparing a 6-qubit cluster state using quantum computers on the cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of optimization, such as circuit identities and error mitigation and…
Analysis of Boolean Functions Related to Binary Input Binary Output Two-party Nonlocal Games
本文穷举四变量布尔函数以表达二元输入二元输出双方非定域博弈，发现除CHSH外部分博弈量子成功率更高，但CHSH博弈在量子和经典技术的分离效率上表现最佳。
Motivated by Buscemi's semi-quantum nonlocal game [PRL 108, 200401(2012)], We propose an entanglement witness game, a quantum game based on entanglement witness. Similar as the semi-quantum nonlocal game, the existence of entanglement shared by the players is necessary and sufficient for obtaining a positive average payoff in our entanglement witness game. Two explicit examples are constructed to demonstrate how to play our entanglement witness game and its relations with the CHSH nonlocal game.
We outline the general construction of three-players games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the exchange of the players; (ii) the existence of the upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)$÷$(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered which is obtained by keeping the same utilities but replacing classi…
If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player's input at the conclusion of the game, he cannot perfectly recover her o…
Monogamy of Nonlocal Games
本文提出一种将贝尔单调性关系从特定配置扩展到所有多人设置的方法，证明CHSH博弈非局域性仅存在于两人和直线四人场景，并首次发现不受量子纠缠单调性影响的非局域博弈。
Quantum nonlocality is an inherently non-classical feature of quantum mechanics and manifests itself through violation of Bell inequalities for nonlocal games. We show that in a fairly general setting, a simple extension of a nonlocal game can certify instead the absence of quantum nonlocality. Through contraposition, our result implies that a super-classical performance for such a game ensures that a player's output is unpredictable to the other player. Previously such output unpredictability was known with respect to a third party.
The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly models a physical system. The simplest instance of a nonlocal game involves two players, Alice and Bob, who are not allowed to communicate with each other once the game has started and who play cooperatively against an adversary referred to as the referee. The focus of this thesis is a class of games called extended nonlocal games, of which nonlocal games are …
This paper considers a special class of nonlocal games $(G,ψ)$, where $G$ is a two-player one-round game, and $ψ$ is a bipartite state independent of $G$. In the game $(G,ψ)$, the players are allowed to share arbitrarily many copies of $ψ$. The value of the game $(G,ψ)$, denoted by $ω^*(G,ψ)$, is the supremum of the winning probability that the players can achieve with arbitrarily many copies of preshared states $ψ$. For a noisy maximally entangled state $ψ$, a two-player one-round game $G$ and an arbitrarily small precision $ε>0$, this paper proves an upper bound on the number of copies of $ψ…
Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states
本文为BCS和XOR等非定域博弈建立了近似刚性结果，证明了近似最优量子策略可逼近使用最大纠缠态的策略，并将该结论推广至同步博弈类。
Post-selection games
本文提出后选择游戏，通过允许裁判舍弃轮次，扩展了非本地游戏，以更有效地分析低检测效率的贝尔测试。
This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication of these examples is that entanglement can profoundly affect the soundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upper bounds may be regarded as gener…
Maximally entangled states are not complete for pseudo-telepathy
该研究针对量子非局域性领域的长期开放性问题，构造了输入集大小为4和3、输出集均为6的双体内积游戏，作为最大纠缠态对于伪心灵感应游戏不完备的反例，证明了最大纠缠态并非此类游戏的完备资源。
Constructive nonlocal games with very small classical values
本文提出围长方法，构造具有极小经典值的线性非局部博弈，并探讨其量子值上界可能导致的量子-经典值最佳比率。
Bell nonlocality is a cornerstone of quantum theory with applications in information processing ranging from cryptography to distributed computing and game theory. Indeed, it is known that Bell's theorem can be formally linked to Bayesian games, allowing the use of nonlocal correlations to advise players and thereby achieve new points of equilibrium that are unavailable classically. Here we generalize this link, proving the connection between multistage games of incomplete information with Bell scenarios involving the communication of measurement outcomes between the parties. We apply the gene…
Nonlocal games with synchronous correlations are a natural generalization of functions between two finite sets. In this work we examine analogues of Bell's inequalities for such correlations, and derive a synchronous device-independent quantum key distribution protocol. This protocol has the advantage of symmetry between the two users and self-testing while generating shared secret key without requiring a preshared secret. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. Howev…
A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games
本文提出非交换零点定理，证明完美量子或交换算子策略的双答案非局部博弈均存在完美经典策略，并推广至无限维情形。
Self-testing a quantum device means verifying the existence of a certain quantum state as well as the effect of the associated measurements based only on the statistics of the measurement outcomes. Robust, i.e., error-tolerant, self-testing quantum devices are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted quantum devices. We give a criterion which determines whether a given binary XOR game is robust self-testing with the asymptotically optimal error parameter. As an application, we prove that the celebrated CHSH game is an optimally robust sel…
Measurement-device-independent Schmidt number certification of all entangled states
本文提出了一种基于半量子非本地游戏的测量设备无关认证方法，用于认证具有高Schmidt数的纠缠态，解决了传统贝尔非本地游戏无法认证所有纠缠态的问题。
A convergent sum-of-squares hierarchy for compiled nonlocal games
本文针对编译型非局部博弈的量子可靠性，扩展良好平方和证书框架，构造收敛至最优量子值的半定规划层级，并统一复现已知界。
Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical scenario for which no finite amount of entanglement suffices. To this end we introduce a simple two-party nonlocal game $H$, inspired by Lucien Hardy's paradox. In our game each player has only two possible questions and can provide bit strings of any finite length as answer. We exhibit a sequence of strategies which use entangled states in inc…
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same, nearest-neighboring gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting for measurement-read…
Playing Nonlocal Games with Little to No Shared Randomness
该研究探讨共享随机性受限的贝尔非局域性经典模型，通过评估线性贝尔泛函刻画无共享随机性的关联，扩展至量子网络时构建非线性不等式，还将其应用于生成有限共享随机性二分场景的熵型贝尔不等式。
We bound separations between the entangled and classical values for several classes of nonlocal $t$-player games. Our motivating question is whether there is a family of $t$-player XOR games for which the entangled bias is $1$ but for which the classical bias goes down to $0$, for fixed $t$. Answering this question would have important consequences in the study of multi-party communication complexity, as a positive answer would imply an unbounded separation between randomized communication complexity with and without entanglement. Our contribution to answering the question is identifying sever…
First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent set games are the hardest instances of this problem. Secondly, we show that if every independent set game whose entangled value is equal to one admits a perfect entangled strategy, then the same holds for all symmetric synchronous games. Finally, we identify combinatorial lower bounds on the classical and entangled values of synchronous games in terms of vari…
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classica…
We introduce a simple transformation on two-player nonlocal games, called "anchoring", and prove an exponential-decay parallel repetition theorem for all anchored games in the setting of quantum entangled players. This transformation is inspired in part by the Feige-Kilian transformation (SICOMP 2000), and has the property that if the quantum value of the original game $G$ is $v$ then the quantum value of the anchored game $G_\bot$ is $1 - (1 - α)^2 \cdot (1 - v)$ where $α$ is a parameter of the transformation. In particular the anchored game has quantum value $1$ if and only if the original g…
Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games
本研究将香农零误差通信概念引入不完全信息博弈，提出零误差纳什均衡协调框架，证明Bell非定域关联可实现经典条件下无法达成的博弈协调，且该优势在实验噪声下依然稳健，搭建了信息论、博弈论与量子非定域性的新桥梁。
Transitive Nonlocal Games
本文研究传递非局部博弈，建立双同步传递博弈与量子置换群的对应，并证明三类策略存在性等价，进而刻画相关关联非局部性的充要条件。
In this work, we explore a new direction by complementing the game-theoretic applications of nonlocal correlations through appropriately formulated games using temporal quantum correlations. In the context of Bayesian games, we show the way temporal correlations can be utilized, thereby leading to quantum strategies that are impossible to simulate in a classical world. Furthermore, by educing some intriguing characteristics of projective measurements performed between two temporally separated measurements on a given system, we also construct some specific types of Biased Bayesian games. Finall…
Robust self-testing for nonlocal games with robust game algebras
本文提出基于C*-代数迹状态唯一性的鲁棒自检验新框架，证明其等价性，并给出首个定量Gowers-Hatami定理以计算显式鲁棒性函数。
Bounding the quantum value of compiled nonlocal games: from CHSH to BQP verification
本文研究了 Kalai 等人提出的非定域博弈密码学编译程序的量子值，证明了 CHSH 博弈在编译后保持 Tsirelson 界及强刚性，并据此构建了更简洁的 BQP 经典验证协议。
Bounds on Multipartite Nonlocality via Reduction to Biased Nonlocality
本文通过LOCCG模型为THRESHOLD游戏提供多方非局域性的最优界，并建立多方非局域性与偏双局域性游戏之间的减少关系。
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 qua…
XOR Games at Full Tilt: The Hardness of Binary Nonlocal Games
研究倾斜异或博弈，其获胜条件可额外取决于一个输出位。证明将其量子值近似到恒定精度的问题计算复杂度是RE完全的，结果扩展到简洁版本。还表明经典策略下二者区别不大，且此归约在量子方面合理，意味着二元博弈近似RE难。
Counterexamples in self-testing
本文通过构造基于博弈选择的显式反例，否定回答了所有具有量子优势的非局域博弈是否都能认证特定量子态以及所有自测试结果是否都能鲁棒化这两个问题。
Buhrman showed that an efficient communication protocol implies a reliable XOR game protocol. This idea rederives Linial and Shraibman's lower bounds of communication complexity, which was derived by using factorization norms, with worse constant factor in much more intuitive way. In this work, we improve and generalize Buhrman's idea, and obtain a class of lower bounds for classical communication complexity including an exact Linial and Shraibman's lower bound as a special case. In the proof, we explicitly construct a protocol for XOR game from a classical communication protocol by using a co…
Quantum bounds for compiled XOR games and $d$-outcome CHSH games
本研究拓展现有证明技术，证实Kalai等人的非局域博弈编译流程可保留XOR博弈与d结果CHSH博弈的量子界，还证明任意量子比特测量对都存在对应XOR博弈，其最优胜率可作为自检测依据。
Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between small computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Our co…
A bound on the quantum value of all compiled nonlocal games
该工作证明所有编译双人非局域游戏的量子值受底层游戏量子交换算子值上界约束，建立了量子可靠性，并引入可能独立有用的序贯刻画技术。
Uncertainty principle is one of the central concepts in quantum theory. Different forms of this particular principle have been discoursed in various foundational and information theoretic topics. In the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by fine-grained uncertainty relation. On the other hand, in continuous variable paradigm Robertson-Schrodinger (RS) uncertainty relation has been used to detect multi-mode entanglement. Here we show that RS uncertainty relation plays an important role to discriminate between quantum and post-quantu…
Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. Here we construct a nonlocal game that can be won with certainty by $2N$ players if they have access to the ground state of the toric code on as many qubits. By contrast, the game cannot be won by classical players more than half the time in the large $N$ limit. Our game differs from previous examples because it arranges the players on a latti…
In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify a spectrahedral outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín (NPA) hierarchy and also a sufficient condition for the set of quantum correlations to b…
Quantum Coordination and Nonlocal Games: Theory and Applications
本文综述经典与量子网络协调的进展，提出含经典/量子通信与预共享关联的统一框架，探讨其在非局部博弈、DI-QKD及量子中继器中的应用，揭示协调理论与相关量子通信应用的关联。
We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the promise problem corresponding to the approximation of the nonlocal value to inverse polynomial accuracy is complete for QMIP*, and therefore NEXP-hard. This establishes that nonlocal games are provably harder than classical games without any complexity theory assumptions. Our result also indicates that gap amplification for nonlocal games may be impossible in ge…
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