Critical assessment of two-qubit post-Markovian master equations

TL;DR

This paper critically evaluates two-qubit post-Markovian master equations, highlighting potential issues with physicality and positivity when extending single-qubit models to two qubits, emphasizing careful application of such models.

Contribution

It extends the analysis of post-Markovian master equations to two qubits, revealing challenges in maintaining physicality and positivity in the extended models.

Findings

Single-qubit post-Markovian dynamics are always physical.

Extension to two qubits can break the positivity of the dynamical map.

Care is needed when applying phenomenological models beyond Markovian assumptions.

Abstract

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.