Guess Your Neighbour’s Input: No Quantum Advantage but an Advantage for Quantum Theory

Acín, Antonio; Almeida, Mafalda L.; Augusiak, Remigiusz; Brunner, Nicolás

doi:10.1007/978-94-017-7303-4_14

Cited by 6 publications

(27 citation statements)

References 56 publications

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“…Consider the causal game where A B C maj , , ( )is the majority of the three bitsA,B, andC. Whenever the majority of the inputs is0, i.e., A B C maj , , 0 ( )= , then the parties play the 'guess-your-neighbours-input' game [57,58]: partyA guesses the input of partyB, partyB guesses the input of partyC, and finally partyC guesses the input of partyA; the game is won if all guesses are correct simultaneously. If the majority of the inputs is1, then they play the same game in reverse direction and flip the output bits.…”

Section: Examplesmentioning

confidence: 99%

The space of logically consistent classical processes without causal order

2016

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Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made, but the processes are restricted to be logically consistent under any choice of the parties' operations. It is known that for three parties or more, this set of processes is larger than the set of processes achievable in a predefined ordering of the parties. Here, we model all classical processes without predefined causal order geometrically and find that the set of such processes forms a polytope. Additionally, we model a smaller polytope-the deterministic-extrema polytope-where all extremal points represent deterministic processes. This polytope excludes probabilistic processes that must be-quite unnaturally-fine-tuned, because any variation of the weights in a decomposition into deterministic processes leads to a logical inconsistency. Motivation and main resultAn assumption often made in physical theories, sometimes implicitly, is the existence of a global time. In particular, quantum theory is formulated with time as an intrinsic parameter. If one relaxes this assumption by requiring local validity of some theory and logical consistency only, then a larger set of correlations can be obtained, called correlations without predefined causal order. The processes that lead to such correlations are called processes without predefined causal order. Two motivations to study such correlations are quantum gravity and quantum non-locality. Quantum gravity motivates this research in the sense that on the one hand, relativity is a deterministic theory equipped with a dynamic spacetime; on the other hand, quantum theory is a probabilistic theory embedded in a fixed spacetime. This suggests that quantum gravity is relaxed in both aspects, i.e.,it is a probabilistic theory equipped with a dynamic spacetime [1]. Quantum non-local correlations [2][3][4] motivate this study since the possibility of a satisfactory causal explanation [5] for such correlations is questionable [3,[6][7][8][9][10][11][12][13]. Dropping the notion of a global time or of an a priori spacetime-as has been suggested from different fields of research[14-23]-dissolves this paradox. This can be achieved by defining causal relations based on free randomness (see figure 1) as opposed to defining free randomness based on causal relations [24,25]. Such an approach gives a dynamic character to causality; causal connections are not predefined but are derived from the observed correlations.Relaxations of quantum theory where the assumption of a global time is dropped have recently been studied widely [1, 26-45] (see [46] for a review). Our work follows the spirit of an operational quantum framework for such correlations developed by Oreshkov et al [31]. Some correlations appearing in their quantum framework -for two parties or more-cannot be simulated by assuming a predefined causal order of the parties. Such correlations ar...

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Section: Examplesmentioning

confidence: 99%

The space of logically consistent classical processes without causal order

2016

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“…This provides convincing evidence that the framework works. We show that the advantage of no-signaling correlations over quantum or classical cases scales to the proven bound 2 [27,29] and the correlations achieving the optimal bound are given. Additionally, we solve analytically the tripartite case completely.…”

Section: Introductionmentioning

confidence: 95%

“…Recently, a nonlocal multipartite scheme GYNI, "guess your neighbor's input", has been presented and investigated in Refs. [27][28][29][30][31][32][33][34][35]. It demonstrates that the no-signaling correlations provide a clear advantage over both classical and quantum correlations, while * Electronic address: muliangzhu@pku.edu.cn † Electronic address: hfan@iphy.ac.cn these two correlations have a common ground in this scheme.…”

Section: Introductionmentioning

confidence: 98%

Classification of no-signaling correlation and the “guess your neighbor's input” game

Wang

Zhou

et al. 2014

Phys. Rev. A

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We formulate a series of non-trivial equalities which are satisfied by all no-signaling correlations, meaning that no faster-than-light communication is allowed with the resource of these correlations. All quantum and classical correlations satisfy these equalities since they are no-signaling. By applying these equalities, we provide a general framework for solving the multipartite "guess your neighbor's input" (GYNI) game, which is naturally no-signaling but shows conversely that general no-signaling correlations are actually more non-local than those allowed by quantum mechanics. We confirm the validity of our method for number of players from 3 up to 19, thus providing convincing evidence that it works for the general case. In addition, we solve analytically the tripartite GYNI and obtain a computable measure of supra-quantum correlations. This result simplifies the defined optimization procedure to an analytic formula, thus characterizing explicitly the boundary between quantum and supra-quantum correlations. In addition, we show that the gap between quantum and no-signaling boundaries containing supra-quantum correlations can be closed by local orthogonality conditions in the tripartite case. Our results provide a computable classification of no-signaling correlations.

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“…with the remaining 40 joint probabilities being all zero. In addition to the nonlocality conditions (21)- (22), the set of probabilities (25) satisfies the modified Hardy-type nonlocality conditions established in [20], which, for the specific case of three-qubit systems, read as…”

Section: Cabello's Nonlocality Argument For Three Qubitsmentioning

confidence: 99%

“…To end this section, we provide yet another probability distribution fulfilling all the conditions Eqs. (18)- (22), for which C = 0.4 (with P = 0.6 and Q = 0.2):…”

Section: Cabello's Nonlocality Argument For Three Qubitsmentioning

confidence: 99%

Cabello’s nonlocality for generalized three-qubit GHZ states

Cereceda

2016

Quantum Stud.: Math. Found.

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In this paper, we study Cabello's nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14% (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy's nonlocality argument (HNA) for three qubits, namely 12.5%. Also, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of 50% in the framework of generalized no-signaling theory.

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Guess Your Neighbour’s Input: No Quantum Advantage but an Advantage for Quantum Theory

Cited by 6 publications

References 56 publications

The space of logically consistent classical processes without causal order

The space of logically consistent classical processes without causal order

Classification of no-signaling correlation and the “guess your neighbor's input” game

Cabello’s nonlocality for generalized three-qubit GHZ states

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