Beyond complete positivity |
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Authors: | Jason M Dominy " target="_blank">Daniel A Lidar |
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Affiliation: | 1.Department of Chemistry,University of Southern California,Los Angeles,USA;2.Department of Physics,University of Southern California,Los Angeles,USA;3.Department of Electrical Engineering,University of Southern California,Los Angeles,USA;4.Center for Quantum Information Science & Technology,University of Southern California,Los Angeles,USA |
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Abstract: | We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any \({\mathbb {C}}\)-linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality. |
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