Critical assessment of two-qubit post-Markovian master equations

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.

7 pages, 1 figure, RevTeX4. Close to published version

References in corpus (6)

• Optimized Dynamical Decoupling in a Model Quantum Memory
• Non-Markovian quantum jumps
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain
• Non-Markovian behavior of small and large complex quantum systems
• Non-Markovian master equations from entanglement with stationary unobserved degrees of freedom

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• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Post-Markovian quantum master equations from classical environment fluctuations
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• Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectiveness
• Commutativity and the emergence of classical objectivity