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arXiv · 1710.10038

Unifying Entanglement with Uncertainty via Symmetries of Observable Algebras

Li Gao·Marius Junge·Nicholas LaRacuente
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Abstract

Strong subadditivity goes beyond the tensored subsystem and commuting operator models. As previously noted by Petz and later by Araki and Moriya, two subalgebras of observables satisfy a generalized SSA-like inequality if they form a commuting square. We explore the interpretation and consequences in finite dimensions, connecting various entropic uncertainty relations for mutually unbiased bases with the positivity of a generalized conditional mutual information (CMI), and with inequalities on relative entropies of coherence and asymmetry. We obtain a bipartite resource theory of operations under which the two subalgebras are respectively invariant and covariant, with CMI as a monotone, and generalized non-classical monotones based on squashed entanglement and entanglement of formation. Free transformations support conversion between entanglement and uncertainty-based configurations, as "EPR <-> 2UCR." Our theory quantifies the common non-classicality in entanglement and uncertainty, implying a strong conceptual link between these fundamentally quantum phenomena.

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Li Gao, Marius Junge, Nicholas LaRacuente. 2017-10-27. Unifying Entanglement with Uncertainty via Symmetries of Observable Algebras. https://arxiv.org/abs/1710.10038

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