Stochastic unravellings of non-Markovian completely positive and trace preserving maps

Abstract

We consider open quantum systems with factorized initial states, providing the structure of the reduced system dynamics, in terms of environment cumulants. We show that such completely positive (CP) and trace preserving (TP) maps can be unraveled by linear stochastic Schrödinger equations (SSEs) characterized by sets of colored stochastic processes (with n-th order cumulants). We obtain both the conditions such that the SSEs provide CPTP dynamics, and those for unraveling an open system dynamics. We then focus on Gaussian non-Markovian unravellings, whose known structure displays a functional derivative. We provide a novel description that replaces the functional derivative with a recursive operatorial structure. Moreover, for the family of quadratic bosonic Hamiltonians, we are able to provide an explicit operatorial dependence for the unravelling.

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Cited by in corpus (10)

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• Mass-coupled relativistic spontaneous collapse models
• Local disclosure of quantum memory in non-Markovian dynamics
• Continuous quantum measurement for general Gaussian unravelings can exist
• On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians
• Channel Discord and Distortion
• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems
• Decoherence Effect of Qubits in 1D Transverse Ising Model