Reliability Function of Quantum Information Decoupling via the Sandwiched R\'enyi Divergence

TL;DR

This paper characterizes the exponential rate at which quantum information decoupling approaches perfection, using sandwiched Re9nyi divergence, with applications to quantum state merging and new bounds for key quantum information measures.

Contribution

It provides an exact formula for the reliability function of quantum decoupling below a critical cost, and bounds for high cost scenarios, linking sandwiched Re9nyi divergence to operational quantum information tasks.

Findings

Exact formula for decoupling reliability function below critical cost

Upper and lower bounds for high decoupling cost scenarios

New bounds for smoothing of conditional min-entropy and max-information

Abstract

Quantum information decoupling is a fundamental quantum information processing task, which also serves as a crucial tool in a diversity of topics in quantum physics. In this paper, we characterize the reliability function of catalytic quantum information decoupling, that is, the best exponential rate under which perfect decoupling is asymptotically approached. We have obtained the exact formula when the decoupling cost is below a critical value. In the situation of high cost, we provide meaningful upper and lower bounds. This result is then applied to quantum state merging, exploiting its inherent connection to decoupling. In addition, as technical tools, we derive the exact exponents for the smoothing of the conditional min-entropy and max-information, and we prove a novel bound for the convex-split lemma. Our results are given in terms of the sandwiched R\'enyi divergence, providing it with a new type of operational meaning in characterizing how fast the performance of quantum information tasks approaches the perfect.