Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras
Keyword(s):
Type I
◽
AbstractWe prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda $$L_p$$ L p norms. We comment on applications to the quantum null energy condition.
2011 ◽
Vol 13
(04)
◽
pp. 643-657
◽
2017 ◽
Vol 29
(07)
◽
pp. 1750020
◽
2002 ◽
Vol 05
(04)
◽
pp. 571-579
◽