Exploiting Finite Geometries for Better Quantum Advantages in Mermin-Like Games
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909137052368896 |
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| author | Kelleher, Colm Holweck, Frédéric Lévay, Péter |
| author_facet | Kelleher, Colm Holweck, Frédéric Lévay, Péter |
| contents | Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no - communication game with certainty, where classical players cannot. In this paper we look at the geometric structure behind such classical strategies, and borrow ideas from the geometry of symplectic polar spaces to maximise this quantum advantage. We introduce a new game called the Eloily game with a quantum-classical success gap of $0.2\overline{6}$, larger than that of the Mermin-Peres and doily games. We simulate this game in the IBM Quantum Experience and obtain a success rate of $1$, beating the classical bound of $0.7\overline{3}$ demonstrating the efficiency of the quantum strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploiting Finite Geometries for Better Quantum Advantages in Mermin-Like Games Kelleher, Colm Holweck, Frédéric Lévay, Péter Quantum Physics Mathematical Physics Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no - communication game with certainty, where classical players cannot. In this paper we look at the geometric structure behind such classical strategies, and borrow ideas from the geometry of symplectic polar spaces to maximise this quantum advantage. We introduce a new game called the Eloily game with a quantum-classical success gap of $0.2\overline{6}$, larger than that of the Mermin-Peres and doily games. We simulate this game in the IBM Quantum Experience and obtain a success rate of $1$, beating the classical bound of $0.7\overline{3}$ demonstrating the efficiency of the quantum strategy. |
| title | Exploiting Finite Geometries for Better Quantum Advantages in Mermin-Like Games |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.09512 |