Saturating the quantum Cram\'er-Rao bound using LOCC

TL;DR

This paper demonstrates that LOCC-based measurements can saturate the quantum Cramér-Rao bound for certain quantum states, highlighting the importance of classical communication in achieving optimal parameter estimation precision.

Contribution

It shows that LOCC measurements, which are practically feasible, can saturate the QCRB for specific classes of quantum states, unlike local measurements without communication.

Findings

LOCC measurements can saturate the QCRB for pure and certain mixed states.

Local measurements alone generally cannot achieve QCRB saturation.

The results clarify the role of classical communication in quantum parameter estimation.

Abstract

The quantum Cram\'er-Rao bound (QCRB) provides an ultimate precision limit allowed by quantum mechanics in parameter estimation. Given any quantum state dependent on a single parameter, there is always a positive-operator valued measurement (POVM) saturating the QCRB. However, the QCRB-saturating POVM cannot always be implemented efficiently, especially in multipartite systems. In this paper, we show that the POVM based on local operations and classical communication (LOCC) is QCRB-saturating for arbitrary pure states or rank-two mixed states with varying probability distributions over fixed eigenbasis. Local measurements without classical communication, however, is not QCRB-saturating in general.