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arXiv · 2507.21630

Complete Positivity of Subsystems in Quantum Dynamics

Anumita Mukhopadhyay·Praggnyamita Ghosh·Shibdas Roy
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Abstract

Although many quantum channels satisfy Completely Positive Trace Preserving (CPTP) condition, there are valid quantum channels that can be non-completely positive (NCP). As memory effects can provide advantages in the dynamics of noisy quantum systems, we investigate the relative CP condition and the CP-divisibility condition of the system and environment subsystems of a joint system-environment quantum state evolving noiselessly. We show that the system and environment channels must be both CP (NCP) or CP-divisible (CP-indivisible) for the evolution in the joint system-environment space to be unitary. We illustrate our results with examples of Bell state created from $|00\rangle$, GHZ state created from $|000\rangle$, W state created from $|100\rangle$, and the partial transpose (PT) operation acting on the Bell state

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Anumita Mukhopadhyay, Praggnyamita Ghosh, Shibdas Roy. 2025-07-29. Complete Positivity of Subsystems in Quantum Dynamics. https://arxiv.org/abs/2507.21630

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