Selective and Efficient Estimation of Parameters for Quantum Process Tomography

We present a new method for quantum process tomography enabling the efficient estimation, with fixed precision, of any of the parameters characterizing a quantum channel. The estimation strategy depends upon the set of matrix elements one selects to estimate. Furthermore, we describe a way to efficiently gather all the information required to efficiently estimate any average survival probability of the channel (i.e., to measure any diagonal element of its $\chi$ matrix).

Figure 1

Circuit for measuring ${\chi }_{mm}$ for a channel $\mathcal{E}$.

Figure 2

Circuit for measuring $\mathrm{Re}({\chi }_{m{m}^{\prime }})$ for a channel $\mathcal{E}$.