English

Map-Dependent Quantum Characteristic Functions and CP-Divisibility in Non-Markovian Quantum Dynamics

Quantum Physics 2026-04-21 v1 Mathematical Physics math.MP

Abstract

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.

Cite

@article{arxiv.2604.17185,
  title  = {Map-Dependent Quantum Characteristic Functions and CP-Divisibility in Non-Markovian Quantum Dynamics},
  author = {Koichi Nakagawa},
  journal= {arXiv preprint arXiv:2604.17185},
  year   = {2026}
}

Comments

5 pages, 6 figures

R2 v1 2026-07-01T12:16:24.352Z