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IEEE International Conference on Computer Sciences and Information Technologies (CSIT)

Computer Simulation for Quantum Tomography

Bohdan Yavorskyy

Published Sep 23, 2020• 0 citations
Publisher

Abstract

Is proposed numerical method for simulation reconstruction quantum states of light's harmonics in homodyne tomography. Had been investigated the homodyne processing of discretized and quantized function of sine that was used as model of light's harmonic. In results were obtained the representations of the squeezed quantum amplitude-phase and vacuum states, as well as vacuum and coherent (displaced) quantum states. The computing simulation model parameters have been identified, and estimated. Graphics images of quantum states are presented; future using of obtained results for quantum tomography are discussed.

DOI
10.1109/csit49958.2020.9322034

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Is proposed numerical method for simulation reconstruction quantum states of light's harmonics in homodyne tomography. Had been investigated the homodyne processing of discretized and quantized function of sine that was used as model of light's harmonic. In results were obtained the representations of the squeezed quantum amplitude-phase and vacuum states, as well as vacuum and coherent (displaced) quantum states. The computing simulation model parameters have been identified, and estimated. Graphics images of quantum states are presented; future using of obtained results for quantum tomography are discussed.
States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.
In this work, a continuous variable quantum tomography is presented. This is done using two approaches, one using simulated data and another one using data from measurements performed in the laboratory. The Radon inverse transform, under the approximation of filtered back projection, alongside the details on the implementa- tion of balanced homodyne detection needed to perform the tomography are clearly explained. Density matrices in the quadrature and number representation are also obtained from the Wigner function. Additionally, complete documentation of the computational implementation and a user-friendly interface for the tomography is reported
This chapter begins with a review of classical tomography, which reconstructs hidden structures inside an object by successive transmissions of an X-ray beam at different angles and lateral displacements. By interpreting the Wigner distribution as an analogue of the density distribution in a physical object, the mathematical methods of classical tomography — the Radon transform, the Fourier slice theorem, and the inverse Radon transform — are adapted to perform a high resolution determination of a quantum state of light. In optical homodyne tomography, the classical transmission angle is replaced by the adjustable phase of a local oscillator, and the successive lateral displacements are replaced by a series of measurements of the quadrature operator defined by the local oscillator phase. Experimental data is presented showing various properties of the Wigner distribution for a coherent state.
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of different observables, obtained on identical copies of the same system. Alternatively, it consists in maximizing an appropriate likelihood function defined on the same data. The procedure can be also used to completely characterize an unknown apparatus. Here we focus on the electromagnetic field, where the tomographic observables are obtained from homodyne detection.