A hazard of open quantum dynamics: Markov approximations encounter map domains

TL;DR

This paper investigates how Markov approximations in open quantum dynamics can lead to unphysical results when the map acts outside its domain, especially in correlated two-qubit systems, highlighting potential issues in repeated applications.

Contribution

The paper provides a detailed analysis of the domain issues in Markov approximations for open quantum systems, illustrating how correlations cause unphysical outcomes in simple two-qubit models.

Findings

Unphysical results occur when Markov maps act outside their domains.

Repeated application of the map can lead to states outside physical bounds.

Correlations between qubits exacerbate the domain issues.

Abstract

A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two interacting qubits, for which the map domains have been described quite completely. A time interval is split into two parts and the map from the exact dynamics for the entire interval is replaced by the conjunction of that same map for both parts. If there is any correlation between the two qubits, unphysical results can appear as soon as the map conjunction is used, even for infinitesimal times. If the map is repeated an unlimited number of times, every state is at risk of being taken outside the bounds of physical meaning. Treatment by slippage of initial conditions is discussed.