The strong converse exponent of composable randomness extraction against quantum side information

TL;DR

This paper precisely characterizes the strong converse exponent for quantum randomness extraction with composable error criteria, linking it to a recently introduced quantum conditional entropy and providing an operational interpretation.

Contribution

It introduces a tight characterization of the strong converse exponent for quantum randomness extraction using a composable error measure, connecting it to a new quantum conditional entropy.

Findings

Provides a tight bound on the strong converse exponent

Links the exponent to a club-sandwiched quantum conditional entropy

First operational interpretation of this entropy family in quantum information

Abstract

We find a tight characterization of the strong converse exponent for randomness extraction against quantum side information. In contrast to previous tight bounds, we employ a composable error criterion given by the fidelity (or purified distance) to a uniform distribution in product with the marginal state. The characterization is in terms of a club-sandwiched conditional entropy recently introduced by Rubboli, Goodarzi and Tomamichel and used by Li, Li and Yu to establish the strong converse exponent for the case of classical side information. This provides the first precise operational interpretation of this family of conditional entropies in the quantum setting.