Non-Markovian Toy Quantum Chain

Abstract

We propose a simple structure for stationary non-Markovian quantum chains in the framework of collisional dynamics of open quantum systems. To this end, we modify the microscopic Markovian system--reservoir model, consider multiple collisions with each of the molecules with an overlap between the collisional time intervals. We show how the equivalent Markovian quantum chain can be constructed with the addition of satellite quantum memory to the system. We distinguish quantum from classical non-Markovianity. Moreover, we define the counts of non-Markovianity by the required number of satellite qubits and bits, respectively. As the particular measure of quantum non-Markovianity the discord of the satellite w.r.t. the system is suggested. Simplest qubit realizations are discussed, and the significance for real system--environment dynamics is also pointed out.

10 pages, 10 figures

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• The multilevel four-stroke swap engine and its environment
• Class of exact memory-kernel master equations
• Witnessing quantum memory in non-Markovian processes
• Crisis of the Chaotic Attractor of a Climate Model: A Transfer Operator Approach
• Thermalization of finite many-body systems by a collision model
• Wigner entropy production and heat transport in linear quantum lattices
• Quantum Critical Probing and Simulation of Colored Quantum Noise
• Semi-device-independent certification of quantum non-Markovianity using sequential Random Access Codes
• Making Quantum Collision Models Exact
• All-optical implementation of collision-based evolutions of open quantum systems