On estimates of the Bures distance between bosonic Gaussian states

TL;DR

This paper extends previous work to derive upper bounds for the Bures distance between bosonic Gaussian states, emphasizing its relevance for quantum state estimation and learning.

Contribution

It introduces improved upper bounds for the Bures distance between Gaussian states, enhancing methods for quantum state estimation.

Findings

Derived upper bounds for Bures distance between Gaussian states

Bounds are better suited for state estimation tasks

Method extends previous results with minimal additional effort

Abstract

The aim of the present note is to show that the method of our paper ArXiv:2408.11400 with minor extra efforts can be extended to obtain upper bounds for the Bures distance between quantum Gaussian states. We argue that these bounds are better adapted to the Bures distance and hence to the state estimation and learning with the Bures distance rather than that with the trace-norm distance.