Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination

• URL: http://arxiv.org/abs/2211.11008v1
• Date: Sun, 20 Nov 2022 15:56:03 GMT
• Title: Complete Positivity Violation in Higher-order Quantum Adiabatic Elimination
• Authors: Masaaki Tokieda, Cyril Elouard, Alain Sarlette, Pierre Rouchon
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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