No-cloning theorem for 2WQC and postselection

Abstract

Two-way quantum computers (2WQC) are proposed extension of standard 1WQC: adding conjugated state preparation operation $\langle 0|$ similar to postselection $|0\ra \langle 0|$, by performing a process which from perspective of CPT symmetry is the original state preparation process, for example by reversing EM impulses used for state preparation. As there were concerns that this extension might violate no-cloning theorem for example for attacks on quantum cryptographic protocols like BB84, here we extend the original proof to show this theorem still holds for 2WQC and postselection.