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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.17185 |
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| _version_ | 1866918454441803776 |
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| author | Nakagawa, Koichi |
| author_facet | Nakagawa, Koichi |
| contents | We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated Gram matrix is equivalent to complete positivity of the underlying quantum channel. Applying the construction to intermediate dynamical maps, we obtain a characterization of CP-divisibility in terms of positivity of two-time characteristic functions. Numerical examples for amplitude damping and pure dephasing models demonstrate that negativity of the Gram matrix coincides with the breakdown of CP-divisibility and the emergence of information backflow. The proposed framework provides a new bridge between characteristic-function methods in quantum statistics and structural properties of quantum dynamical maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Map-Dependent Quantum Characteristic Functions and CP-Divisibility in Non-Markovian Quantum Dynamics Nakagawa, Koichi Quantum Physics Mathematical Physics We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated Gram matrix is equivalent to complete positivity of the underlying quantum channel. Applying the construction to intermediate dynamical maps, we obtain a characterization of CP-divisibility in terms of positivity of two-time characteristic functions. Numerical examples for amplitude damping and pure dephasing models demonstrate that negativity of the Gram matrix coincides with the breakdown of CP-divisibility and the emergence of information backflow. The proposed framework provides a new bridge between characteristic-function methods in quantum statistics and structural properties of quantum dynamical maps. |
| title | Map-Dependent Quantum Characteristic Functions and CP-Divisibility in Non-Markovian Quantum Dynamics |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2604.17185 |