Strong Converse Exponent of Quantum Dichotomies

TL;DR

This paper investigates the large-deviation behavior of quantum dichotomies, establishing the first exact strong converse exponent in the fully quantum setting based on the purified distance.

Contribution

It provides the first precise large-deviation analysis and determines the exact strong converse exponent for quantum dichotomies.

Findings

Established the exact strong converse exponent for quantum dichotomies.

Performed the first high-error large-deviation analysis in a fully quantum context.

Connected the rate of quantum state transformations to large-deviation principles.

Abstract

The quantum dichotomies problem asks at what rate one pair of quantum states can be approximately mapped into another pair of quantum states. In the many copy limit and for vanishing error, the optimal rate is known to be given by the ratio of the respective quantum relative distances. Here, we study the large-deviation behavior of quantum dichotomies and determine the exact strong converse exponent based on the purified distance. This is the first time to establish the exact high-error large-deviation analysis for this task in fully quantum setting.