Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

TL;DR

This paper analyzes the estimation of damping and temperature in Gaussian dissipative channels, showing two-mode squeezed vacuum states achieve optimal precision and outperform other states, with non-Gaussian states also offering advantages.

Contribution

It demonstrates the optimality of two-mode squeezed vacuum states for estimating damping and temperature simultaneously in Gaussian channels, and compares their performance with non-Gaussian states.

Findings

Two-mode squeezed vacuum states achieve quantum-limited accuracy for both parameters.

These states outperform coherent, thermal, and single-mode squeezed states in high-energy regimes.

Certain non-Gaussian states with high entanglement perform better than less entangled states of similar energy.

Abstract

We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than either coherent, thermal or single-mode squeezed states. This suggests that at high energy regimes two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within D-dimensional cutoff subspaces perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.