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arXiv · 1503.05342

Beyond Complete Positivity

Jason M. Dominy·Daniel A. Lidar
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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 subsystem 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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Jason M. Dominy, Daniel A. Lidar. 2015-03-18. Beyond Complete Positivity. https://arxiv.org/abs/1503.05342

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