[Paper Review] Operational significance of nonclassicality in nonequilibrium Gaussian quantum thermometry

Safoura S. Mirkhalaf, Mohammad Mehboudi+2 more|arXiv (Cornell University)|Jul 21, 2022

Advanced Thermodynamics and Statistical Mechanics4 citations

TL;DR

This paper proposes a fully Gaussian protocol for nonequilibrium quantum thermometry using nonclassical probe states—specifically single-mode and two-mode squeezed vacuum states—under Gaussian dynamics. It demonstrates that nonclassicality enables a significant improvement over classical limits in temperature estimation, even with Gaussian measurements, offering a practical and operationally meaningful advantage in continuous-variable quantum platforms.

ABSTRACT

We provide new operational significance of nonclassicality in nonequilibrium temperature estimation of bosonic baths with Gaussian probe states and Gaussian dynamics. We find a bound on the thermometry performance using classical probe states. Then we show that by using nonclassical probe states, single-mode and two-mode squeezed vacuum states, one can profoundly improve the classical limit. Interestingly, we observe that this improvement can also be achieved by using Gaussian measurements. Hence, we propose a fully Gaussian protocol for enhanced thermometry, which can simply be realized and used in quantum optics platforms.

Motivation & Objective

• To establish the operational significance of nonclassicality in nonequilibrium Gaussian quantum thermometry with continuous-variable systems.
• To identify the fundamental limit of classical probe states in temperature estimation under Gaussian dynamics.
• To demonstrate that nonclassical Gaussian probe states and Gaussian measurements can surpass this classical limit.
• To propose a fully Gaussian, experimentally feasible protocol for enhanced thermometry in quantum optics and related platforms.

Proposed method

• The study models a probe mode interacting with a thermal bath via Gaussian dynamics, described as Brownian motion with a time-dependent coupling.
• It uses single-mode and two-mode squeezed vacuum states as initial probe states to exploit nonclassical correlations.
• The protocol employs a 50:50 beamsplitter followed by homodyne measurements on the output modes to perform a joint Gaussian measurement.
• The classical Fisher information (CFI) is computed from the covariance matrix of the post-interaction state, quantifying the estimation precision.
• The CFI is evaluated for both classical and nonclassical probes, with the latter showing a substantial improvement over the classical bound.
• The analysis is conducted in the framework of continuous-variable quantum information, leveraging the Gaussian formalism for exact analytical treatment.

Experimental results

Research questions

• RQ1 Can nonclassical Gaussian probe states provide a measurable advantage in nonequilibrium temperature estimation compared to classical probes?
• RQ2 What is the fundamental performance limit of classical Gaussian probes in nonequilibrium thermometry under fixed time resources?
• RQ3 Can this advantage be achieved using only Gaussian measurements, without requiring nonlinear or non-Gaussian operations?
• RQ4 To what extent does entanglement between probe and ancillary modes enhance thermometric precision in a Gaussian framework?
• RQ5 How does the use of squeezed states affect the Fisher information in a dynamical, non-equilibrium setting?

Key findings

• The classical probe limit is rigorously bounded, showing that classical Gaussian states cannot achieve optimal thermometric precision in nonequilibrium scenarios.
• Single-mode and two-mode squeezed vacuum states significantly surpass the classical limit, demonstrating that nonclassicality enhances estimation sensitivity.
• The improvement is maintained even when using only Gaussian measurements, such as a 50:50 beamsplitter followed by homodyne detection.
• The classical Fisher information for the Gaussian protocol scales favorably with interaction time and squeezing parameter, showing a quadratic improvement in precision over classical probes.
• The protocol is fully realizable in quantum optical platforms, making it experimentally accessible for continuous-variable thermometry.
• The analytical expression for the classical Fisher information is derived in closed form, enabling direct comparison between classical and nonclassical regimes.