Surpassing the Thermal Cramer-Rao Bound with Collisional Thermometry

TL;DR

This paper investigates how to optimize ancilla states in collisional thermometry to surpass the thermal Cramér-Rao bound, demonstrating conditions for quantum advantage with collective measurements and energy exchange channels.

Contribution

It refines previous analyses by optimizing ancilla states, including block-i.i.d. states, and identifies when collective measurements outperform single-copy strategies.

Findings

Optimal ancilla states can beat the thermal Cramér-Rao bound.

Collective measurements provide advantages for N>1 ancillas.

Energy exchange channels enable surpassing classical limits.

Abstract

In collisional thermometry, a system in contact with the thermal bath is probed by a stream of ancillas. Coherences and collective measurements were shown to improve the Fisher information in some parameter regimes, for a stream of independent and identically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett., 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimising over the possible input ancilla states, also for block-i.i.d.~states of block size b=2. For both an indirect measurement interaction and a coherent energy exchange channel, we show when the thermal Cram\'er-Rao bound can be beaten, and when a collective measurement of $N>1$ ancilla may return advantages over single-copy measurements.