Complete positivity on the subsystems level
arXiv:1708.07873 · doi:10.1007/s10773-018-3864-6
Abstract
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely positive and trace preserving maps, with the constraint that domain of the map is the whole Banach space of the system's density matrices. We provide a technically simple and conceptually clear proof for the subsystems' completely positive dynamics. Actually, we prove that every subsystem of a composite open system can be subject of a completely positive dynamics if and only if the initial state of the composite open system is tensor-product of the initial states of the subsystems. An algorithm for obtaining the Kraus form for the subsystem's dynamical map is provided. As an illustrative example we consider a pair of mutually interacting qubits. The presentation is performed such that a student with the proper basic knowledge in quantum mechanics should be able to reproduce all the steps of the calculations.
revised ms, improved presentation, 18 pages, no tables or figures
References in corpus (10)
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Vanishing quantum discord is necessary and sufficient for completely positive maps
- Does coherence enhance transport in photosynthesis?
- Finding the Kraus decomposition from a master equation and vice versa
- Vanishing quantum discord is not necessary for completely-positive maps
- Gravity-related spontaneous collapse in bulk matter
- Dissipation in the Caldeira-Leggett model
- Quantum thermodynamics of nanoscale steady states far from equilibrium
- Kraus operators for a pair of interacting qubits: a case study
- Dynamical stability of the one-dimensional rigid Brownian rotator: The role of the rotator's spatial size and shape