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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.11205 |
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| _version_ | 1866917696048726016 |
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| author | Watanabe, Akane Suzuki, Takayuki Unoki, Makoto Nakazato, Hiromichi |
| author_facet | Watanabe, Akane Suzuki, Takayuki Unoki, Makoto Nakazato, Hiromichi |
| contents | The complete positivity (CP) of a quantum dynamical map (QDM) is, in general, difficult to show when its master equation (ME) does not conform to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The GKSL ME describes the Markovian dynamics, comprising a unitary component with time-independent Hermitian operators and a non-unitary component with time-independent Lindblad operators and positive time-independent damping rates. Recently, the non-Markovian dynamics has received growing attention, and the various types of GKSL-like MEs with time-dependent operators are widely discussed; however, rigorous discussions on their CP conditions remain limited. This paper presents conditions for QDMs to be CP, whose MEs take the GKSL-like form with arbitrary time dependence. One case considered is where its ME takes the time-local integro-differential GKSL-like form, which includes CP-divisible cases. Another case considered is where the ME is time-non-local but can be approximated to be time-local in the weak-coupling regime. As a special case of the time-non-local case, the same discussion holds for the time-convoluted GKSL-like form, which should be compared to previous studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CP conditions for GKSL-like master equations Watanabe, Akane Suzuki, Takayuki Unoki, Makoto Nakazato, Hiromichi Quantum Physics The complete positivity (CP) of a quantum dynamical map (QDM) is, in general, difficult to show when its master equation (ME) does not conform to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The GKSL ME describes the Markovian dynamics, comprising a unitary component with time-independent Hermitian operators and a non-unitary component with time-independent Lindblad operators and positive time-independent damping rates. Recently, the non-Markovian dynamics has received growing attention, and the various types of GKSL-like MEs with time-dependent operators are widely discussed; however, rigorous discussions on their CP conditions remain limited. This paper presents conditions for QDMs to be CP, whose MEs take the GKSL-like form with arbitrary time dependence. One case considered is where its ME takes the time-local integro-differential GKSL-like form, which includes CP-divisible cases. Another case considered is where the ME is time-non-local but can be approximated to be time-local in the weak-coupling regime. As a special case of the time-non-local case, the same discussion holds for the time-convoluted GKSL-like form, which should be compared to previous studies. |
| title | CP conditions for GKSL-like master equations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.11205 |