TY - JOUR

T1 - Approximate recoverability and relative entropy II

T2 - 2-positive channels of general von Neumann algebras

AU - Faulkner, Thomas

AU - Hollands, Stefan

N1 - Funding Information:
SH is grateful to the Max-Planck Society for supporting the collaboration between MPI-MiS and Leipzig U., grant Proj. Bez. M.FE.A.MATN0003. He thanks Felix Otto for discussion and R. Longo for suggesting a connection with the index. TF and SH benefited from the KITP program “Gravitational Holography” which was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. TF acknowledges part of the work presented here is supported by the DOE under grant DE-SC0019517 as well as the Air Force Office of Scientific Research under award number FA9550-19-1-0360.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/4

Y1 - 2022/4

N2 - We generalize our results in paper I in this series 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.

AB - We generalize our results in paper I in this series 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.

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U2 - 10.1007/s11005-022-01510-9

DO - 10.1007/s11005-022-01510-9

M3 - Article

AN - SCOPUS:85126285287

SN - 0377-9017

VL - 112

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

M1 - 26

ER -