# A squeezing invariant measurement to test displacement of quantum Gaussian states

## TL;DR

This paper introduces a quantum measurement method invariant under squeezing operations to test displacement parameters of Gaussian states, comparing its effectiveness with classical heterodyne-based tests.

## Contribution

It develops a squeezing-invariant quantum measurement for hypothesis testing of displacement parameters in Gaussian states, providing a new approach for quantum state analysis.

## Key findings

- Calculated the type II error probability for pure states.
- Demonstrated the invariance property of the measurement under squeezing.
- Compared the quantum test with classical heterodyne-based tests.

## Abstract

We consider a hypothesis testing problem for displacement parameters of n independent copies of an m-mode squeezed quantum Gaussian state whose mixture parameter is known. Given n>1, we construct a quantum measurement as a test using an observable which is invariant by n-fold tensor product of any m-mode squeezing operator. For a pure state case, we calculate the type II error probability of this test. We compare this test with a Hotelling's T-squared test which is based on heterodyne measurements.