  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.
