dorsal/arxiv
View SchemaPlaying games in quantum mechanical settings: A necessary and sufficient condition
| Authors | Junichi Shimamura, Sahin Kaya Ozdemir, Nobuyuki Imoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508105 |
| URL | https://arxiv.org/abs/quant-ph/0508105 |
Abstract
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy, 2x2, dilemma containing classical games, and transferred them into quantum realm showing that in quantum pure strategies dilemmas in such games can be resolved if entanglement is distributed between the players armed with quantum operations. Moreover, it became clear that the 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": "A number of recent studies have focused on novel features in game theory when\nthe games are played using quantum mechanical toolbox (entanglement, unitary\noperators, measurement). Researchers have concentrated in two-player-two\nstrategy, 2x2, dilemma containing classical games, and transferred them into\nquantum realm showing that in quantum pure strategies dilemmas in such games\ncan be resolved if entanglement is distributed between the players armed with\nquantum operations. Moreover, it became clear that the players receive the\nhighest sum of payoffs available in the game, which are otherwise impossible in\nclassical pure strategies. Encouraged by the observation of rich dynamics of\nphysical systems with many interacting parties and the power of entanglement in\nquantum versions of 2x2 games, it became generally accepted that quantum\nversions can be easily extended to N-player situations by simply allowing\nN-partite entangled states. In this article, however, we show that this is not\ngenerally true because the reproducibility of classical tasks in quantum domain\nimposes limitations on the type of entanglement and quantum operators. We\npropose a benchmark for the evaluation of quantum and classical versions of\ngames, and derive the necessary and sufficient conditions for a physical\nrealization. We give examples of entangled states that can and cannot be used,\nand the characteristics of quantum operators used as strategies.",
"arxiv_id": "quant-ph/0508105",
"authors": [
"Junichi Shimamura",
"Sahin Kaya Ozdemir",
"Nobuyuki Imoto"
],
"categories": [
"quant-ph"
],
"title": "Playing games in quantum mechanical settings: A necessary and sufficient condition",
"url": "https://arxiv.org/abs/quant-ph/0508105"
},
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