Reduced dynamical maps in the presence of initial correlations

Abstract

We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by considering the marginals with respect to the environmental degrees of freedom of the considered class of correlated states. Our approach allows to consider states whose discord is not necessarily zero and explicitly show the non-uniqueness of the completely positive extensions of the obtained dynamical map outside the compatibility domain. The relevance of such maps for the treatment of open quantum system dynamics is discussed and connection to previous literature is critically assessed.

10 pages, 1 figure

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• Causal classification of spatiotemporal quantum correlations
• A weak-coupling master equation for arbitrary initial conditions
• Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments
• Distinguishing between statistical and systematic errors in quantum process tomography
• Completely Positive Maps for Reduced States of Indistinguishable Particles
• Sufficient Conditions and Constraints for Reversing General Quantum Errors
• Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems
• When the assignment map is completely positive
• Guaranteeing Completely Positive Quantum Evolution
• Dynamics of Open Quantum Systems with Initial System-Environment Correlations via Stochastic Unravelings
• Non-Markovian open dynamics from collision models
• Complete positivity on the subsystems level
• On the use of total state decompositions for the study of reduced dynamics
• Adapted projection operator technique for the treatment of initial correlations