Permissible four-strategy quantum extensions of classical games
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912023661510656 |
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| author | Frąckiewicz, Piotr Gorczyca-Goraj, Anna Szopa, Marek |
| author_facet | Frąckiewicz, Piotr Gorczyca-Goraj, Anna Szopa, Marek |
| contents | The study focuses on strategic-form games extended in the Eisert-Wilkens-Lewenstein scheme by two unitary operations. Conditions are determined under which the pair of unitary operators, along with classical strategies, form a game invariant under isomorphic transformations of the input classical game. These conditions are then applied to determine these operators, resulting in five main classes of games satisfying the isomorphism criterion, and a theorem is proved providing a practical criterion for this isomorphism. The interdependencies between different classes of extensions are identified, including limit cases in which one class transforms into another. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Permissible four-strategy quantum extensions of classical games Frąckiewicz, Piotr Gorczyca-Goraj, Anna Szopa, Marek Quantum Physics Computer Science and Game Theory The study focuses on strategic-form games extended in the Eisert-Wilkens-Lewenstein scheme by two unitary operations. Conditions are determined under which the pair of unitary operators, along with classical strategies, form a game invariant under isomorphic transformations of the input classical game. These conditions are then applied to determine these operators, resulting in five main classes of games satisfying the isomorphism criterion, and a theorem is proved providing a practical criterion for this isomorphism. The interdependencies between different classes of extensions are identified, including limit cases in which one class transforms into another. |
| title | Permissible four-strategy quantum extensions of classical games |
| topic | Quantum Physics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2405.07380 |