A study of LOCC-detection of a maximally entangled state using hypothesis testing

We study how well we can answer 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.