Direct Characterization of Quantum Dynamics

The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative “direct characterization of quantum dynamics” (DCQD) algorithm. In contrast to all known QPT methods, this algorithm relies on error-detection techniques and does not require any quantum state tomography. We illustrate that, by construction, the DCQD algorithm can be applied to the task of obtaining partial information about quantum dynamics. Furthermore, we argue that the DCQD algorithm is experimentally implementable in a variety of prominent quantum-informatiom processing systems, and show how it can be realized in photonic systems with present day technology.

Figure 1

Schematic of characterization algorithm for the single-qubit case, consisting of Bell-state preparations, applying the unknown quantum map, $\mathcal{E}$, and BSM.

Figure 2

A schematic layout of a linear-optical realization of the DCQD algorithm. A pair of entangled photons, $(|H_A{H}_B⟩+e^{i\phi }|V_A{V}_B⟩)/\sqrt{2}$, is generated via parametric down-conversion in a nonlinear crystal from a UV pump laser, where $|H⟩$ and $|V⟩$ represent horizontal and vertical polarization [12]. The quarter and half wave plates are used to create nonmaximally entangled states [18], and change the preparation and measurement bases. Two-photon interferometry occurs at the $50/50$ beam splitters. This allows for discriminating two of the four Bell states deterministically, by utilizing polarizing beam splitters and photodetectors as analyzers.