ИСТИНА

An experimental realization of an adaptive quantum state tomography protocol for high-dimensional states is presented. A Bayesian inference is utilized to estimate the state and its properties of interest (purity, concurrence, an accuracy of the estimation). We compare our adaptive approach with random measurements which are known to be optimal in a non-adaptive case. We observe a qualitative enhancement in the estimation accuracy. The scaling of the Bures distance (which is used as a figure of merit) for pure states is close to N^{-1} with overall number of registered events N, while the non-adaptive measurements gives close to N^{-1/2} scaling. Also the adaptivity yields faster in an estimating the properties of the state. Experiments are performed with polarization degrees of freedom of biphotons produced during a spontaneous down-conversion process with a degenerate noncollinear phase matching. We use a scheme with two BBO crystals having their optical axes perpendicular. It allows to vary an entanglement of the state from factorized one to the Bell state by rotating a linear polarization of a pump. The purity can be altered by changing collecting irises diameter. Only factorized measurements are carried in the experiment. The performance of entangled measurements (i.e. with no constraints imposed) is investigated by means of simulations. In a case when both the experiment and the simulations can be applied (factorized measurements) they coincide with each other. The results show that factorized adaptive measurements outperform entangled random measurements (the Bures distance scaling N^{-1.0} vs N^{-0.6} correspondingly). Previously the adaptive tomography was studied experimentally only for the case of qubits [1,2] and this work is an extension towards ququarts, and the proposed algorithm is versatile and can be applied to a system of arbitrary dimension. [1] K.S.Kravtsov, S.S.Straupe, I.V.Radchenko, N.M.T.Houlsby, F.Huszar, and S.P.Kulik "Experimental adaptive Bayesian tomography". Phys. Rev. A. 87, 062122 (2013) [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)