  Motivated by successful classical models for noise reduction, we suggest a
quantum technique for filtering noise out of quantum states. The purpose of
this paper is twofold: presenting a simple construction of quantum
cross-correlations between two wave-functions, and presenting a scheme for a
quantum noise filtering. We follow a well-known scheme in classical
communication theory that attenuates random noise, and show that one can build
a quantum analog by using non-trace-preserving operators. By this we introduce
a classically motivated signal processing scheme to quantum information theory,
which can help reducing quantum noise, and particularly, phase flip noise.
