On the rational invariants of quantum systems of $n$-qubits
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916156760129536 |
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| author | Candelori, Luca Chernyak, Vladimir Y. Klein, John R. |
| author_facet | Candelori, Luca Chernyak, Vladimir Y. Klein, John R. |
| contents | For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree $4^n - 2n-1$. An explicit transcendence basis is also exhibited. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06346 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rational invariants of quantum systems of $n$-qubits Candelori, Luca Chernyak, Vladimir Y. Klein, John R. Mathematical Physics Quantum Algebra Rings and Algebras Representation Theory Quantum Physics 81P40, 81P42, 13A50, 14L24 For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree $4^n - 2n-1$. An explicit transcendence basis is also exhibited. |
| title | On the rational invariants of quantum systems of $n$-qubits |
| topic | Mathematical Physics Quantum Algebra Rings and Algebras Representation Theory Quantum Physics 81P40, 81P42, 13A50, 14L24 |
| url | https://arxiv.org/abs/2403.06346 |