Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras

Abstract:We establish the exact exponent for smoothing the max-relative entropy on arbitrary von Neumann algebras. The proof first develops the required large-deviation and smoothing estimates in the semifinite setting and then passes to general von Neumann algebras through Haagerup-Junge-Xu reduction. We next study catalytic quantum information decoupling when the reference system is described by an arbitrary von Neumann algebra. A key ingredient is an operator layer-cake formula valid on arbitrary von Neumann algebras. This formula leads to a convex-split estimate for normal states with a general von Neumann algebraic reference system. Combining this estimate with the smoothing exponent result, we obtain lower and upper bounds on the catalytic-decoupling reliability function. These bounds coincide below the corresponding critical rate, yielding the exact decoupling reliability function in that regime.

Information Theory (cs.IT); Operator Algebras (math.OA); Quantum Physics (quant-ph)

arXiv:2607.07997 [cs.IT]

(or arXiv:2607.07997v2 [cs.IT] for this version)

https://doi.org/10.48550/arXiv.2607.07997 Focus to learn more arXiv-issued DOI via DataCite

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