Complete Positivity of Subsystems in Quantum Dynamics

• URL: http://arxiv.org/abs/2507.21630v2
• Date: Wed, 30 Jul 2025 09:11:19 GMT
• Title: Complete Positivity of Subsystems in Quantum Dynamics
• Authors: Anumita Mukhopadhyay, Praggnyamita Ghosh, Shibdas Roy,
• Abstract summary: We study the relation of complete positivity (CP) with unitality, where a map must be non-unital in order to be NCP.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although many quantum channels satisfy Completely Positive Trace Preserving (CPTP) condition, there are valid quantum channels that can be non-completely positive (NCP). In a search of the conditions of noisy evolution to be a useful resource for quantum computing, we study the relation of complete positivity (CP) with unitality, where we find that a map must be non-unital in order to be NCP, but not vice-versa. 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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