ИСТИНА

Adaptive measurements have recently been shown to significantly improve accuracy of quantum state and process tomography compared to conventional techniques. By definition in adaptive protocols future measurements depend on the data previously obtained. The measurements are chosen in an optimal way according to some criterion. Tomography of high-dimensional systems itself is a computationally involved problem, therefore adaptive criterion should be simple enough to allow fast measurement selection. On the other hand, measurement choice should result in high reconstruction accuracy of the true state. Moreover, an adaptive scheme should be flexible, i. e. it can be easily tailored to use only some subset of experimentally available measurements. A selected subset in high-dimensional multipartite tomography is factorized measurements, namely, local measurements of subsystems. We mainly focus on the simplest case of bipartite systems. In our opinion there is lack of computationally fast protocols for high-dimensional tomography, that utilize only factorized measurements. For example, Bayesian optimal experimental design is a versatile approach with high reconstruction accuracy, but it is computationally involved [1]. A prominent class of protocols include measurements in the eigenbasis of the current estimate [2]. The problem is that the eigenbasis will almost certainly contain entangled vectors, and therefore these protocols require general type of measurements, which is a severe experimental limitation. There is no straightforward generalization of these protocols to include solely factorized measurements. We propose a novel adaptive protocol [3], which is both computationally fast and relies only on factorized measurements, and still improves reconstruction accuracy. The protocol is especially advantageous for true states that can be treated as low-rank ones (this includes the important for applications case of pure states). The idea behind the protocol is to select measurements with nearly zero outcome probability, whenever it is possible. We provide arguments that such measurements, called orthogonal measurements, are necessary to qualitatively improve the estimation accuracy compared to non-adaptive protocols. We investigate the performance of the proposed protocol in both numerical simulations and real experiments for the states with dimension up to 36. In experiments the true state is encoded in spatial degrees of freedom of photon pairs produced by a spontaneous parametric down conversion. We compare our protocol with random measurement strategy (experiment and simulations) and protocols based on measurements in the eigenbasis (simulations). We use a maximum likelihood estimation (MLE) for data processing, however, our protocol is independent of the choice of a statistical estimation procedure. We observe an improvement of reconstruction accuracy for our protocol, compared to the non-adaptive random measurements. 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, L. A. Rozema, A. Darabi, C. Ferrie, R. Blume-Kohout, and A. M. Steinberg. "Adaptive Quantum State Tomography Improves Accuracy Quadratically". Phys. Rev. Lett., 111, 183601, 2013. 3. G. I. Struchalin, E. V. Kovlakov, S. S. Straupe, and S. P. Kulik. "Adaptive quantum tomography of high-dimensional bipartite systems". arXiv:1804.05226 [quant-ph], 2018.