  For one-dimensional PT -symmetric systems, it is observed that the non-local
product obtained from the continuity equation can be interpreted as a conserved
corre- lation function. This leads to physical conclusions, regarding both
discrete and continuum states of such systems. Asymptotic states are shown to
have necessarily broken PT -symmetry, leading to modified scattering and
transfer matrices. This yields restricted boundary conditions, e.g., in-
cidence from both sides, analogous to that of the proposed PT CPA laser. The
interpretation of left and right states leads to a Hermitian S-matrix,
resulting in the non-conservation of the flux. This further satisfies a duality
condition, identical to the optical analogues. However, the non-local conserved
scalar implements alternate boundary conditions in terms of in and out states,
leading to the pseudo-Hermiticity condition in terms of the scattering matrix.
Interestingly, when PT -symmetry is preserved, it leads to stationary states
with real energy, naturally inter- pretable as bound states. The broken PT
-symmetric phase is also captured by this correlation, with complex-conjugate
pair of energies, interpreted as resonances.
