  We show that a quantum system possessing an exact antilinear symmetry, in
particular PT-symmetry, is equivalent to a quantum system having a Hermitian
Hamiltonian. We construct the unitary operator relating an arbitrary
non-Hermitian Hamiltonian with exact PT-symmetry to a Hermitian Hamiltonian. We
apply our general results to PT-symmetry in finite-dimensions and give the
explicit form of the above-mentioned unitary operator and Hermitian Hamiltonian
in two dimensions. Our findings lead to the conjecture that non-Hermitian
CPT-symmetric field theories are equivalent to certain nonlocal Hermitian field
theories.
