On the variety of X-states
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916140878397440 |
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| author | Candelori, Luca Chernyak, Vladimir Y. Klein, John R. |
| author_facet | Candelori, Luca Chernyak, Vladimir Y. Klein, John R. |
| contents | We introduce the notion of an X-state on $n$-qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety $\scr X$ that is equipped with the action of the Lie group of local symmetries $G$. We show that the field of $G$-invariant rational functions on $\scr X$ is purely transcendental over the complex numbers of degree $2^{2n-1}-n-1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the variety of X-states Candelori, Luca Chernyak, Vladimir Y. Klein, John R. Mathematical Physics Algebraic Geometry Quantum Algebra Quantum Physics Primary: 81P40, 81P42, 13A50, Secondary: 14L24 We introduce the notion of an X-state on $n$-qubits. After taking the Zariski closure of the set of X-states in the space of all mixed states, we obtain a complex algebraic variety $\scr X$ that is equipped with the action of the Lie group of local symmetries $G$. We show that the field of $G$-invariant rational functions on $\scr X$ is purely transcendental over the complex numbers of degree $2^{2n-1}-n-1$. |
| title | On the variety of X-states |
| topic | Mathematical Physics Algebraic Geometry Quantum Algebra Quantum Physics Primary: 81P40, 81P42, 13A50, Secondary: 14L24 |
| url | https://arxiv.org/abs/2402.17181 |