Environment-Assisted Quantum State Restoration Via Weak Measurement

Abstract: In this paper, a new quantum state restoration scheme is proposed based on the environment-assisted error correction (EAEC) scheme. By introducing a weak measurement reversal (WMR) operation, we shall show how to recover an initial state of a quantum open system without invoking random unitary decompositions which are known to be absent in many important physical systems. We illustrate our new scheme and compare it with a scheme purely based on the WMR operation in the case of dissipative channel. In the proposed new scheme, the successful probability of recovering an unknown initial state can be significantly improved when the information obtained from an environment measurement is taken into account. Moreover, we show that the applicable range of our proposed scheme is wider than the EAEC scheme. Finally, the optimization of the successful probability for possible Kraus decompositions is discussed.