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Approximate recoverability and relative entropy II: 2-positive channels of general v. Neumann algebras

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arxiv 2010.05513 v1 pith:CAHHC7SK submitted 2020-10-12 quant-ph hep-th

Thomas Faulkner , Stefan Hollands This is my paper · ORCID
classification quant-phhep-th
keywords algebraschannelentropyneumannrelativeapproximatechangechannels
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We generalize our results in paper I in this series to quantum channels between general v. Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end, we derive a strengthened form of the quantum data processing inequality for the change in relative entropy of two states under a channel between two v. Neumann algebras. Compared to the usual inequality, there is an explicit lower bound involving the fidelity between the original state and a recovery channel.

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Cited by 2 Pith papers

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  1. Algebras for generalized entanglement wedges

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    Generalized (Bousso–Penington) entanglement wedges are conjectured to carry von Neumann algebras such that S_gen(W) = S(ω|A_W) − log Ind(E) + K_Ω (eq. 2.7), making BP's monotonicity and strong subadditivity consequenc...

  2. Combinatorial aspects of holographic quantum secret sharing

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