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Quantum tomograph for measurement and characterization of quantum states of biphoton sources

Dmitry N. Frolovtsev, Sergey A Magnitskiy, Andrey V. Demin

Published Apr 1, 2020• 1 citation
Publisher

Abstract

The method and prototype of a device for characterizing of biphoton light sources based on spontaneous parametric downdonversion by quantum tomography are described. The prototype is an experimental implementation of a specialized quantum tomograph designed to measure the quantum polarization states of radiation generated by biphoton sources. Specially developed software will determine the statistical characteristics of the measured quantum state, calculate the tomographic and likelihood estimations of the density matrix, calculate the measurement errors of the density matrix elements and evaluate the quality of the quantum state of biphotons.

DOI
10.32446/0368-1025it.2020-4-20-26

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The method and prototype of a device for characterizing of biphoton light sources based on spontaneous parametric downdonversion by quantum tomography are described. The prototype is an experimental implementation of a specialized quantum tomograph designed to measure the quantum polarization states of radiation generated by biphoton sources. Specially developed software will determine the statistical characteristics of the measured quantum state, calculate the tomographic and likelihood estimations of the density matrix, calculate the measurement errors of the density matrix elements and evaluate the quality of the quantum state of biphotons.
The process of quantum tomography of polarization-entangled photon pairs was simulated on quantum computers of different generations of the IBM Q Experience platform. The simulation was carried out for all four two-qubit Bell states. It turned out that the contribution of basis states that are absent in Bell states does not exceed 10 %\%% even on quantum computers of the first generations, and is reduced to several percent on quantum computers of the latest generation. The simulation quality was evaluated using Fidelity. The Fidelity values were in a range of 68.6–94.9 %\%% , depending on the generation of computers. It was shown that for Bell states Fidelity can be calculated using three tomographic measurements instead of the nine required for determination of the density matrix using quantum state tomography.
The essence and basic structural elements of the method of polarization tomography of quantum radiation (the reconstruction of the polarization states of a field solely from polarization measurements) are described. The essential features of the method are discussed in comparison with usual field and spin tomographies. A general scheme for experimentally implementing this method is suggested and its use in polarization tomography of biphotonic radiation with hidden polarization is briefly analyzed.
The works devoted to studying the polarization properties of a two-photon light generated upon spontaneous parametric down-conversion in the collinear frequency-degenerate regime are briefly overviewed, with emphasis on the studies carried out by us over a period from 1999 to 2001 within the framework of the project “Polarization Optics of Biphotons” of the Russian Foundation for Basic Research. In particular, the polarization state of a two-photon light was analyzed and its pictorial mapping onto the Poincaré sphere was proposed. The experiments on polarization transformations of a two-photon light were performed; based on these transformations, a method was suggested for ternary quantum information coding. A two-photon state with the orthogonal photon polarizations was synthesized experimentally from the two beams of identically polarized correlated photons, and the spectral properties of this state were investigated. Finally, a method was suggested for measuring the polarization state of a two-photon light in the collinear frequency-degenerate case (“tomography”).