How to improve the semicontinuity bounds in [Lett. Math. Phys., 113, 121 (2023)]

TL;DR

This paper enhances semicontinuity bounds in mathematical physics by optimizing proof techniques, leading to improved bounds for von Neumann entropy and entanglement of formation under specific constraints.

Contribution

It introduces an optimized proof method that refines existing semicontinuity bounds for key quantum information measures.

Findings

Improved semicontinuity bounds for von Neumann entropy with energy constraints

Enhanced bounds for entanglement of formation considering rank and energy constraints

Application of a modified proof trick to optimize technical lemmas

Abstract

We show how to improve the semicontinuity bounds in [1] by optimizing the proof of the basic technical lemma. In this optimization we apply the modified version of the trick used in the resent article [2]. The most important applications are the semicontinuity bound for the von Neumann entropy with the energy constraint and the semicontinuity bounds for the entanglement of formation with the rank/energy constraint.