Optimal strategies for transient and equilibrium quantum thermometry using Gaussian and non-Gaussian probes

TL;DR

This paper investigates quantum thermometry using Gaussian and non-Gaussian probes in transient and equilibrium regimes, demonstrating how different quantum states and measurements influence temperature estimation precision.

Contribution

It introduces new strategies for quantum thermometry with non-Gaussian states and compares measurement techniques, highlighting the advantages of entanglement and squeezing.

Findings

Non-Gaussian probes accelerate estimation at short times.

Entangled two-mode states enable earlier temperature information access.

Energy-based measurements achieve near-optimal precision.

Abstract

We study temperature estimation using quantum probes, including single-mode initial states and two-mode states generated via stimulated parametric down-conversion in a nonlinear crystal at finite temperature. We explore both transient and equilibrium regimes and compare the performance of Gaussian and non-Gaussian probe states for temperature estimation. In the non-equilibrium regime, we show that single-mode non-Gaussian probe states - such as Fock, odd cat, and Gottesman-Kitaev-Preskill states - can significantly enhance the speed of estimation, particularly at short interaction times. In the two-mode setting, entangled states such as the two-mode squeezed vacuum, NOON state, and entangled cat state can enable access to temperature information at earlier times. In the equilibrium regime, we analyze temperature estimation using two-mode squeezed thermal states, which outperform single-mode strategies. We evaluate practical measurement strategies and find that energy-based observables yield optimal precision, population difference observables provide near-optimal precision, while quadrature-based measurements are suboptimal. The precision gain arises from squeezing, which suppresses fluctuations in the population difference.