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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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Acknowledgments

This research was supported by the ARO MURI Grant W911NF-11-1-0268. The authors thank Iman Marvian for many helpful discussions.

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Correspondence to Daniel A. Lidar.

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Dominy, J.M., Lidar, D.A. Beyond complete positivity. Quantum Inf Process 15, 1349–1360 (2016). https://doi.org/10.1007/s11128-015-1228-1

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