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arXiv:1403.4280

Quantum bidding in Bridge

Sadiq Muhammad, Armin Tavakoli, Maciej Kurant, Marcin Pawłowski, Marek Żukowski, Mohamed Bourennane

Published Mar 17, 2014• 0 citations
arXivHTMLPDF

Abstract

Quantum methods allow to reduce communication complexity of some computational tasks, with several separated partners, beyond classical constraints. Nevertheless, experimental demonstrations of this fact are thus far limited to some abstract problems, far away from real-life tasks. We show here, and demonstrate experimentally, that the power of reduction of communication complexity can be harnessed to gain advantage in famous, immensely popular, card game - Bridge. The essence of a winning strategy in Bridge is efficient communication between the partners. The rules of the game allow only specific form of communication, of a very low complexity (effectively one has a strong limitations on number of exchanged bits). Surprisingly, our quantum technique is not violating the existing rules of the game (as there is no increase in information flow). We show that our quantum Bridge auction corresponds to a biased nonlocal Clauser-Horne-Shimony-Holt (CHSH) game, which is equivalent to a $2\to 1$ quantum random access code. Thus our experiment is also a realization of such protocols. However, this correspondence is not full which enables the Bridge players to have efficient strategies regardless of the quality of their detectors.

DOI
10.48550/arxiv.1403.4280

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Quantum methods allow to reduce communication complexity of some computational tasks, with several separated partners, beyond classical constraints. Nevertheless, experimental demonstrations of this fact are thus far limited to some abstract problems, far away from real-life tasks. We show here, and demonstrate experimentally, that the power of reduction of communication complexity can be harnessed to gain advantage in famous, immensely popular, card game - Bridge. The essence of a winning strategy in Bridge is efficient communication between the partners. The rules of the game allow only specific form of communication, of a very low complexity (effectively one has a strong limitations on number of exchanged bits). Surprisingly, our quantum technique is not violating the existing rules of the game (as there is no increase in information flow). We show that our quantum Bridge auction corresponds to a biased nonlocal Clauser-Horne-Shimony-Holt (CHSH) game, which is equivalent to a 2→12\to 12→1 quantum random access code. Thus our experiment is also a realization of such protocols. However, this correspondence is not full which enables the Bridge players to have efficient strategies regardless of the quality of their detectors.
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.
Quantum pseudotelepathy is a strong form of nonlocality. Different from the conventional nonlocal games where quantum strategies win statistically, e.g., the Clauser-Horne-Shimony-Holt game, quantum pseudotelepathy in principle allows quantum players to with probability 1. In this Letter, we report a faithful experimental demonstration of quantum pseudotelepathy via playing the nonlocal version of Mermin-Peres magic square game, where Alice and Bob cooperatively fill in a 3×3 magic square. We adopt the hyperentanglement scheme and prepare photon pairs entangled in both the polarization and the orbital angular momentum degrees of freedom, such that the experiment is carried out in a resource-efficient manner. Under the locality and fair-sampling assumption, our results show that quantum players can simultaneously win all the queries over any classical strategy.
Demonstrating quantum communication complexity superiority non-trivially with currently available experimental systems is of utmost importance in quantum information science. Here, we propose a generalized entanglement-assisted communication complexity reduction protocol and analyze the robustness of its quantum superiority against the measurement imperfections, such as measurement basis deviation and choice probability bias, a common problem rarely studied before. We find that the quantum superiority can be obtained in a specific entangled state in a suitable range of measurement basis and basis choice parameters. And the quantum superiority strengthens with the increase of the entanglement degree of quantum states. By using the maximum entangled state and its corresponding optimal measurement, the result we obtained violated the optimal classical bound by 239 standard deviations. Besides, the robustness of effective measurement basis in dephasing and depolarizing quantum channels is also investigated. These results not only make a step forward in investigating sufficient experimental conditions to unambiguously demonstrate the superiority of quantum communication complexity but also help to develop relevant practical applications.
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We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed from the player who moves first to the player who moves second. Within this setting, we explore the usage of quantum entanglement between the players and find analytic and numerical conditions for quantum advantage over classical strategies. Using these conditions, we study a family of blackjack-type games with varying numbers of card types, and find a range of parameters where quantum advantage is achieved.