Ancilla-Assisted Quantum Process Tomography

Complete and precise characterization of a quantum dynamical process can be achieved via the method of quantum process tomography. Using a source of correlated photons, we have implemented several methods, each investigating a wide range of processes, e.g., unitary, decohering, and polarizing. One of these methods, ancilla-assisted process tomography (AAPT), makes use of an additional “ancilla system,” and we have theoretically determined the conditions when AAPT is possible. Surprisingly, entanglement is not required. We present data obtained using both separable and entangled input states. The use of entanglement yields superior results, however.

Figure 1

Experimental arrangements to perform quantum process tomography. A 351-nm pump is directed through two 0.6 mm-thick BBO crystals, giving rise to pairs of correlated photons at 702 nm, detected using Si avalanche photodiodes and fast coincidence electronics. $A$, $B$, and $C$ above denote which elements are present for SQPT, EAPT, and nonentangled AAPT, respectively. (a) SQPT: Polarizer (P), half-wave plate (HWP) and quarter-wave plate (QWP) allow preparation of required pure single photon (conditioned on “trigger” detection) states; identical elements allow tomography of the post-process states. (b) EAPT: The source produces the maximally entangled state $(|HH⟩-|VV⟩)/\sqrt{2}$. A two-photon tomography of the output allows reconstruction of the process. (c) AAPT: The source produces ${\rho }_W\sim \frac{1}{6}I+\frac{1}{3}|\gamma ⟩⟨\gamma |$, where $|\gamma ⟩$ is a maximally entangled state. Although there is no entanglement, the correlations in ${\rho }_W$ allow AAPT.

Figure 2

Geometric mappings for three quantum processes—(a) identity, (b) unitary transformation, and (c) decoherence—measured using SQPT (left), EAPT (center), and AAPT (right). The axes are the Stokes parameters ($S_1$, $S_2$, $S_3$). The colored mesh surfaces show how all pure states are transformed by the process. The initial states $H$, $R$, $V$, and $A$ are shown by the green, red, yellow, and blue dots, respectively. The transformation of initial mixed states (inside the surface) may be interpolated from the pure state results using the linearity of quantum mechanics. The mesh coloring denotes the orientation of the transformed sphere.

Figure 3

$\chi$ matrices determined from EAPT for (a) unitary and (b) decohering processes, as shown in Fig. 2.

Figure 4

Geometric mappings and $\chi$ matrices for (a) coherent and (b) incoherent partially polarizing processes. The former was implemented using two glass microscope slides near Brewster’s angle [$T_H\sim 88\%,T_V\sim 45\%$]. The latter was simulated by inserting a horizontal polarizer 50% of the time. (Real components shown; imaginary contributions $<1\%$.)