Environment-assisted quantum state restoration via weak measurements

In this paper, a quantum state restoration scheme is proposed based on the environment-assisted error correction (EAEC) scheme. By introducing a weak measurement reversal (WMR) operation, we will 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 scheme and compare it with a scheme purely based on the WMR operation in the case of a dissipative channel. In the proposed scheme, the successful probability for 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.

Figure 1

Sketch of the EA-WMR scheme.

Figure 2

The ratio $\frac{P_{\mathrm{WM}}}{P_{\mathrm{EW}}}$ at different times $t$ with different initial states ($1\ge \alpha \ge 0$). The initial states are given by $\left|\psi \right(0)\rangle =\alpha |00\rangle +\beta |11\rangle$. It is clear that this ratio always is smaller than 1, which means that the environment-assisted error correction scheme always gives a higher successful probability.

Figure 3

Successful probability for all the possible Kraus decompositions. The parameter $\delta$ is in units of radians.