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Интеллектуальная Система Тематического Исследования НАукометрических данных 

There are two main goals in protocol development for quantum tomography. The first one is to find protocols with minimal number of measurement operators (e.g. minimal qubit tomography based on tetrahedron geometry [1]). The second objective is to construct protocols that achieve a certain level of accuracy faster (compared by the number of measured input states) than others, or equivalently give more accurate estimation for the same number of measured copies of the true state. The present work considers the latter case. Adaptive measurements have recently been shown to significantly improve accuracy of quantum state and process tomography. There exist various adaptive schemes for measurement selection demonstrating different flexibility and computational simplicity. By flexibility we mean that a protocol can be easily tailored to use only some subset of available measurements. The flexibility becomes important when the system of interest is multipartite, because in this case all measurements are divided into two classes: general measurements and factorized measurements (according to a tensor product structure of the system Hilbert space). Factorized measurements carried out on the subsystems independently are relatively simple to implement in experiments, so a protocol, limited to factorized measurements only, is highly desirable. In our opinion there is a lack of flexible and computationally fast protocols for highdimensional state tomography. For example, Bayesian optimal experimental design is a versatile approach with high reconstruction accuracy, but it is computationally involved. A prominent class of computationally fast protocols are protocols that 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 which use factorized measurements only. We present a novel adaptive protocol, which is computationally fast and requires only factorized measurements [3]. We provide arguments that measurements having nearly zero outcome probability for nearly pure states (more precisely, the probability should be less than the minimal eigenvalue of the true state) are necessary to qualitatively improve the estimation accuracy compared to nonadaptive protocols. Therefore the main idea of our protocol is to find vectors to project on that are simultaneously orthogonal to several eigenvectors of the current estimator. We mainly consider a case of bipartite systems with two identical parts, however some results are applicable for general multipartite systems. We investigate the estimation accuracy of the proposed protocol both in numerical simulations and real experiments for the states with dimension up to 36. The experiments are carried out with spatial states of photon pairs produced by a spontaneous parametric down conversion process. In experiments we compare the performance of our protocol with nonadaptive random measurements. In simulations, protocols based on measurements in the eigenbasis are also used for comparison. 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 nonadaptive random measurements both in simulations and in real experiments. [1] J. Řeháček, B.G. Englert, D. Kaszlikowski "Minimal qubit tomography". Phys. Rev. A 70, 052321 (2004) [2] D. H. Mahler, Lee A. Rozema, Ardavan Darabi, Christopher Ferrie, Robin BlumeKohout, and A. M. Steinberg "Adaptive Quantum State Tomography Improves Accuracy Quadratically", Phys. Rev. Lett. 111, 183601 (2013) [3] G. Struchalin, E. Kovlakov, S. Straupe, S. Kulik "Adaptive quantum tomography of highdimensional bipartite systems". arXiv:1804.05226 [quantph] (2018)