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

• URL: http://arxiv.org/abs/2010.05513v1
• Date: Mon, 12 Oct 2020 08:09:17 GMT
• Title: Approximate recoverability and relative entropy II: 2-positive channels of general v. Neumann algebras
• Authors: Thomas Faulkner, Stefan Hollands
• Abstract summary: We prove the approximate recoverability of states which undergo a small change in relative entropy through a quantum channel. 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 Neumann algebras.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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