dorsal/arxiv
View SchemaInvestigations in quantum games using EPR-type set-ups
| Authors | Azhar Iqbal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604188 |
| URL | https://arxiv.org/abs/quant-ph/0604188 |
Abstract
Research in quantum games has flourished during recent years. However, it seems that opinion remains divided about their true quantum character and content. For example, one argument says that quantum games are nothing but 'disguised' classical games and that to quantize a game is equivalent to replacing the original game by a different classical game. The present thesis contributes towards the ongoing debate about quantum nature of quantum games by developing two approaches addressing the related issues. Both approaches take Einstein-Podolsky-Rosen (EPR)-type experiments as the underlying physical set-ups to play two-player quantum games. In the first approach, the players' strategies are unit vectors in their respective planes, with the knowledge of coordinate axes being shared between them. Players perform measurements in an EPR-type setting and their payoffs are defined as functions of the correlations, i.e. without reference to classical or quantum mechanics. Classical bimatrix games are reproduced if the input states are classical and perfectly anti-correlated, as for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. The second approach uses the result that when the predictions of a Local Hidden Variable (LHV) model are made to violate the Bell inequalities the result is that some probability measures assume negative values. With the requirement that classical games result when the predictions of a LHV model do not violate the Bell inequalities, our analysis looks at the impact which the emergence of negative probabilities has on the solutions of two-player games which are physically implemented using the EPR-type experiments.
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"abstract": "Research in quantum games has flourished during recent years. However, it\nseems that opinion remains divided about their true quantum character and\ncontent. For example, one argument says that quantum games are nothing but\n\u0027disguised\u0027 classical games and that to quantize a game is equivalent to\nreplacing the original game by a different classical game. The present thesis\ncontributes towards the ongoing debate about quantum nature of quantum games by\ndeveloping two approaches addressing the related issues. Both approaches take\nEinstein-Podolsky-Rosen (EPR)-type experiments as the underlying physical\nset-ups to play two-player quantum games. In the first approach, the players\u0027\nstrategies are unit vectors in their respective planes, with the knowledge of\ncoordinate axes being shared between them. Players perform measurements in an\nEPR-type setting and their payoffs are defined as functions of the\ncorrelations, i.e. without reference to classical or quantum mechanics.\nClassical bimatrix games are reproduced if the input states are classical and\nperfectly anti-correlated, as for a classical correlation game. However, for a\nquantum correlation game, with an entangled singlet state as input,\nqualitatively different solutions are obtained. The second approach uses the\nresult that when the predictions of a Local Hidden Variable (LHV) model are\nmade to violate the Bell inequalities the result is that some probability\nmeasures assume negative values. With the requirement that classical games\nresult when the predictions of a LHV model do not violate the Bell\ninequalities, our analysis looks at the impact which the emergence of negative\nprobabilities has on the solutions of two-player games which are physically\nimplemented using the EPR-type experiments.",
"arxiv_id": "quant-ph/0604188",
"authors": [
"Azhar Iqbal"
],
"categories": [
"quant-ph"
],
"title": "Investigations in quantum games using EPR-type set-ups",
"url": "https://arxiv.org/abs/quant-ph/0604188"
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