Optimal probe states for the estimation of Gaussian unitary channels

TL;DR

This paper presents a practical method for identifying optimal Gaussian probe states for estimating parameters of Gaussian unitary channels, enhancing precision through temperature control and differences.

Contribution

The paper introduces a comprehensive method to find all optimal Gaussian probe states for parameter estimation, surpassing previous focus on specific states.

Findings

Increasing probe temperature improves estimation precision.

Larger temperature differences between modes enhance accuracy.

The method applies to various Gaussian channels, including phase-change and squeezing.

Abstract

We construct a practical method for finding optimal Gaussian probe states for the estimation of parameters encoded by Gaussian unitary channels. This method can be used for finding all optimal probe states, rather than focusing on the performance of specific states as shown in previous studies. As an example, we apply this method to find optimal probes for the channel that combines the phase-change and squeezing channels, and for generalized two-mode squeezing and mode-mixing channels. The method enables a comprehensive study of temperature effects in Gaussian parameter estimation. It has been shown that the precision in parameter estimation using single mode states can be enhanced by increasing the temperature of the probe. We show that not only higher temperature, but also larger temperature differences between modes of a Gaussian probe state can enhance the estimation precision.