  Bender et al. have developed PT-symmetric quantum theory as an extension of
quantum theory to non-Hermitian Hamiltonians. We show that when this model has
a local PT symmetry acting on composite systems it violates the non-signaling
principle of relativity. Since the case of global PT symmetry is known to
reduce to standard quantum mechanics, this shows that the PT-symmetric theory
is either a trivial extension or likely false as a fundamental theory.
