Hyperentanglement-Enabled Direct Characterization of Quantum Dynamics

We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as direct characterization of quantum dynamics. Specifically, hyperentanglement-assisted Bell-state analysis enabled us to characterize a variety of single-qubit quantum processes using far fewer experimental configurations than are required by standard quantum process tomography. Furthermore, we demonstrate how known errors in Bell-state measurement may be compensated for in the data analysis. Using these techniques, we have obtained single-qubit process fidelities over 98% but with one-third the number of experimental configurations required for standard quantum process tomography. Extensions of these techniques to multiqubit quantum processes are discussed.

Figure 1

The basic measurement schemes for SQPT (a) and DCQD (b) for a single-qubit process $ϵ$. Though DCQD requires more complex input states and measurement settings than SQPT, it also requires 3 times fewer experimental configurations. The dotted boxes before and after the process in (b) represent errors in source preparation and analysis, here described by initial and final error processes (${ϵ}_i$ and ${ϵ}_f$).

Figure 2

(a) Experimental setup used to perform DCQD on various single-qubit quantum processes with hyperentangled photons. A half-wave plate (HWP) tunes the pump polarization to generate photon pairs for SQPT or DCQD. The DCQD input polarization states were prepared with liquid crystals (polarization control). (b) The spin-orbit CNOT gates, which were used to measure the four single-photon hybrid-entangled Bell states in Eq. (5). The outputs of a forked binary hologram are combined on a polarizing beam splitter (PBS) and then spatially filtered with single-mode fibers (SMF).

Figure 3

Reconstructed $\chi$ matrices (absolute values of elements) from SQPT (left column) and DCQD (right column) measurements for the following: identity (a), ${\sigma }_z$ rotation (b), partial dephasing (c), partial polarizer (d), depolarization (e), and simultaneous spin-lattice and spin-spin relaxation (f). The fidelities listed on the right compare the target process with the experimentally measured process using SQPT ($F_J^{\mathrm{SQPT}}$), the target process with the experimentally measured processes using DCQD ($F_J^{\mathrm{DCQD}}$), and the experimentally measured processes using SQPT and DCQD ($F_J^{\mathrm{joint}}$). Uncertainties were calculated using Monte Carlo methods applied to Poissonian photon counting statistics.