Decomposable dynamics on matrix algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915003602305024 |
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| author | Siudzińska, Katarzyna Szczygielski, Krzysztof |
| author_facet | Siudzińska, Katarzyna Szczygielski, Krzysztof |
| contents | We explore a notion of decomposably divisible (D-divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56, 485202 (2023). Both necessary and sufficient conditions are presented for highly-symmetric qubit and qudit dynamical maps. Through a restructurization of the evolution generators, we encode the decomposable divisibility into the positivity of time-dependent coefficients that multiply generators of D-divisible dynamical maps. This provides an analogy to the CP-divisibility property, which is equivalent to the positivity of decoherence rates that multiply Markovian semigroup generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decomposable dynamics on matrix algebras Siudzińska, Katarzyna Szczygielski, Krzysztof Quantum Physics Mathematical Physics We explore a notion of decomposably divisible (D-divisible) quantum evolution families, recently introduced in J. Phys. A: Math. Theor. 56, 485202 (2023). Both necessary and sufficient conditions are presented for highly-symmetric qubit and qudit dynamical maps. Through a restructurization of the evolution generators, we encode the decomposable divisibility into the positivity of time-dependent coefficients that multiply generators of D-divisible dynamical maps. This provides an analogy to the CP-divisibility property, which is equivalent to the positivity of decoherence rates that multiply Markovian semigroup generators. |
| title | Decomposable dynamics on matrix algebras |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2411.01712 |