dorsal/arxiv
View SchemaA necessary and sufficient condition to play games in quantum mechanical settings
| Authors | Sahin Kaya Ozdemir, Junichi Shimamura, Nobuyuki Imoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703006 |
| URL | https://arxiv.org/abs/quant-ph/0703006 |
| DOI | 10.1088/1367-2630/9/2/043 |
| Journal | New Journal of Physics, 9 (2007) 43 |
Abstract
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two strategy (2x2) dilemma containing classical games into quantum realm, dilemmas can be resolved in quantum pure strategies if entanglement is distributed between the players who use quantum operations. Moreover, players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2x2 games, it became generally accepted that quantum versions can be easily extended to N-player situations by simply allowing N-partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
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"abstract": "Quantum game theory is a multidisciplinary field which combines quantum\nmechanics with game theory by introducing non-classical resources such as\nentanglement, quantum operations and quantum measurement. By transferring\ntwo-player-two strategy (2x2) dilemma containing classical games into quantum\nrealm, dilemmas can be resolved in quantum pure strategies if entanglement is\ndistributed between the players who use quantum operations. Moreover, players\nreceive the highest sum of payoffs available in the game, which are otherwise\nimpossible in classical pure strategies. Encouraged by the observation of rich\ndynamics of physical systems with many interacting parties and the power of\nentanglement in quantum versions of 2x2 games, it became generally accepted\nthat quantum versions can be easily extended to N-player situations by simply\nallowing N-partite entangled states. In this article, however, we show that\nthis is not generally true because the reproducibility of classical tasks in\nquantum domain imposes limitations on the type of entanglement and quantum\noperators. We propose a benchmark for the evaluation of quantum and classical\nversions of games, and derive the necessary and sufficient conditions for a\nphysical realization. We give examples of entangled states that can and cannot\nbe used, and the characteristics of quantum operators used as strategies.",
"arxiv_id": "quant-ph/0703006",
"authors": [
"Sahin Kaya Ozdemir",
"Junichi Shimamura",
"Nobuyuki Imoto"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.soc-ph"
],
"doi": "10.1088/1367-2630/9/2/043",
"journal_ref": "New Journal of Physics, 9 (2007) 43",
"title": "A necessary and sufficient condition to play games in quantum mechanical settings",
"url": "https://arxiv.org/abs/quant-ph/0703006"
},
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