  It is shown that the ensemble $\{p (\alpha),|\alpha>|\alpha^*>\}$ where $p
(\alpha)$ is a Gaussian distribution of finite variance and $| \alpha>$ is a
coherent state can be better discriminated with an entangled measurement than
with any local strategy supplemented by classical communication. Although this
ensemble consists of products of quasi-classical states, it exhibits some
quantum nonlocality. This remarkable effect is demonstrated experimentally by
implementing the optimal local strategy together with a joint nonlocal strategy
that yields a higher fidelity.
