Quantum process estimation via generic two-body correlations

Performance of quantum process estimation is naturally limited by fundamental, random, and systematic imperfections of preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction because standard data-analysis techniques usually presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for the estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty-state generators and analyzers. Specifically, we present a generalization of the work begun by M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that for several physically relevant noisy preparations and measurements, classical correlations and a small data-processing overhead suffice to accomplish the full system identification. Furthermore, we provide the optimal input states whereby the error amplification due to inversion of the measurement data is minimal.

Figure 1

Schematic of a faulty DCQD, with imperfect or noisy BSP and BSM.

Figure 2

Value of $|det\mathit{\Lambda }|$ vs $\theta$ and $\phi$. Here, the coefficient matrix $\mathit{\Lambda }(\theta ,\phi )$ relates the experimental outcomes to the unknown elements of the superoperator $|{\mathit{\chi }}^{(\mathrm{T})})=\mathit{\Lambda }|\mathit{\chi })$. The input states for the standard DCQD, as defined in Table , for example, $|{\Phi }_{\alpha }^{+}\rangle =\alpha |00\rangle +\beta |11\rangle$, are parameterized as $\alpha =\cos \theta$ and $\beta =e^{i\phi }\sin \theta$ ($\phi \ne k\pi$, $k\in \mathbb{Z}$). The optimal input states are associated to those parameters for which $|det\mathit{\Lambda }|$ has its maximal value 1, leading to a minimal statistical error.