  We study how well answer to the question ``Is the given quantum state equal
to a certain maximally entangled state?'' using LOCC, in the context of
hypothesis testing. Under several locality and invariance conditions, optimal
tests will be derived for several special cases by using basic theory of group
representations. Some optimal tests are realized by performing quantum
teleportation and checking whether the state is teleported. We will also give a
finite process for realizing some optimal tests. The performance of the tests
will be numerically compared.
