Testing quantum circuits and detecting insecure encryption

Abstract

We show that the computational problem of testing the behaviour of quantum circuits is hard for the class QMA of problems that can be verified efficiently with a quantum computer. This result generalizes techniques previously used to prove the hardness of other problems on quantum circuits.We use this result to show the QMA-completeness of a weak version of the problem of detecting the insecurity of a symmetrickey quantum encryption system or alternately the problem of determining when a quantum channel is not private. © Springer-Verlag Berlin Heidelberg 2013.