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Open Quantum Systems Decoherence

Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination

arXiv

Authors: Masaaki Tokieda, Cyril Elouard, Alain Sarlette, Pierre Rouchon

Year

2022

Paper ID

6666

Status

Preprint

Abstract Read

~2 min

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Abstract

When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow timescales, the description of slow dynamics can be simplified by discarding fast degrees of freedom. This model reduction technique is called adiabatic elimination. While second-order perturbative expansion with respect to the timescale separation has revealed that the evolution of a reduced state is completely positive, this paper presents an example exhibiting complete positivity violation in the fourth-order expansion. Despite the non-uniqueness of slow dynamics parametrization, we prove that complete positivity cannot be ensured in any parametrization. The violation stems from correlation in the initial state.

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When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow timescales, the description of slow dynamics can be simplified by discarding fast...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2211.11008 [2] arXiv https://arxiv.org/abs/2211.11008 [3] Publisher https://arxiv.org/abs/2211.11008

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