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Approximate recoverability and relative entropy. II: 2-positive channels of general von Neumann algebras. (English) Zbl 1495.46052

Summary: We generalize our results in Part I of this series [T. Faulkner et al., Commun. Math. Phys. 389, No. 1, 349–397 (2022; Zbl 1525.46038)] to quantum channels between general von 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 von Neumann algebras. Compared to the usual inequality, there is an explicit lower bound involving the fidelity between the original state and a recovery channel.

MSC:

46L51 Noncommutative measure and integration
46L10 General theory of von Neumann algebras
94A17 Measures of information, entropy
81P40 Quantum coherence, entanglement, quantum correlations
94A40 Channel models (including quantum) in information and communication theory

Citations:

Zbl 1525.46038
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References:

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