ИСТИНА

We present an experimental realization of an adaptive single-qubit process quantum tomography. One of the main goals in quantum tomography in general is to achieve the best accuracy of an estimation. Previous results for state tomography [1,2] show that superior accuracy can be obtained by performing adaptive measurements. This type of measurements utilizes information gathered about the system on preceding steps to adjust the next measurements, in contrast to non-adaptive (static or random) measurements, which have no connection with the state under estimation. In the present work we port adaptive techniques to the case of process tomography. Quantum processes are described in terms of the black box approach which is widely used, e.g., in the field of quantum communication. In this approach internal evolution of a quantum state is irrelevant and only input-output relations are specified. The estimation of an unknown process chi-matrix is carried via Bayesian inference. The posterior distribution entropy minimization criterion is utilized to find the next measurement on-line [3]. We compare the accuracy of the estimate with random measurements, which are known to be optimal in a non-adaptive case. The Bures distance between the estimated and the "true" chi-matrices is used as a figure of merit. We study the performance of the tomography for all types of single-qubit processes both in simulations and in experiments: unitary, partly and fully depolarizing channels, processes with losses and trace-preserving ones. Experiments are carried with polarization degrees of freedom of heralded single photons produced by spontaneous down-conversion process with collinear phase matching. We use a Sagnac interferometer scheme with periodically polarized nonlinear crystal (PPKTP). A thin quartz wave plate represents unitary process; a multimode fiber appears as an example of an (almost) fully depolarizing channel, because different modes acquire different phase shifts, which leads to effective depolarization; a liquid crystal wave plate with time dependent phase shift allows to vary a degree of depolarization by changing the magnitude of a phase shift modulation; a polarizer and a neutral filter are processes with losses. We observe an enhancement of reconstruction quality for the adaptive protocol compared to a random one in the case of rank-1 quantum processes, which include an important class of unitary channels. This behaviour is similar to the case of quantum states, where only pure and near-pure states enjoy benefit from adaptive measurements. Also adaptive tomography is found to be less sensitive to instrumental noise presented in the measurement setup. We discuss the criteria, based on monitoring the chi-squared test statistics, for evaluation of the ultimate achievable precision in an experiment. [1] G. I. Struchalin, I. A. Pogorelov, S. S. Straupe, I. V. Radchenko, K. S. Kravtsov, and S. P. Kulik "Experimental adaptive quantum tomography of two-qubit states". Phys. Rev. A 93, 012103 (2016) [2] D. H. Mahler, Lee A. Rozema, Ardavan Darabi, Christopher Ferrie, Robin Blume-Kohout, and A. M. Steinberg "Adaptive Quantum State Tomography Improves Accuracy Quadratically", Phys. Rev. Lett. 111, 183601 (2013) [3] F. Huszár and N. M. T. Houlsby "Adaptive Bayesian quantum tomography". Phys. Rev. A 85, 052120 (2012)