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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reconstructing a quantum state of light by means of the degree of linear polarization

Łukasz Michalik, Andrzej W. Domański

Published Dec 18, 2012• 1 citation
Publisher

Abstract

In this paper authors present a novel idea for reconstructing quantum states of polarized optical field expressed in the one-photon basis. The quantum state reconstruction is a measurement of a quasidistribution function P that allows to obtain a density operator for the analyzed state. The most commonly used approach for a quantum state reconstruction is based on the so called quantum tomography. The marginal probability distributions for the Wigner function are measured for different angles of projection and then they are put together into the two-dimensional distribution by the inverse Radon transformation. In our approach the analyzed field is combined with the reference field which is well defined, it can be for example a photon-beam containing linearly polarized photons only. The proposed thought experiment assumes that we measure the degree of linear polarization of this combined beam using a rotating polarizer. We obtain the searched distribution P by changing the parameters of the reference beam – its intensity and state of polarization. This series of measurements allows to build the system of equations The values of the function P at various points P(θ i, ϕ j) are the searched variables of this system. Accuracy of that solution depends on how many measurements are done.

DOI
10.1117/12.2007132

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In this paper authors present a novel idea for reconstructing quantum states of polarized optical field expressed in the one-photon basis. The quantum state reconstruction is a measurement of a quasidistribution function P that allows to obtain a density operator for the analyzed state. The most commonly used approach for a quantum state reconstruction is based on the so called quantum tomography. The marginal probability distributions for the Wigner function are measured for different angles of projection and then they are put together into the two-dimensional distribution by the inverse Radon transformation. In our approach the analyzed field is combined with the reference field which is well defined, it can be for example a photon-beam containing linearly polarized photons only. The proposed thought experiment assumes that we measure the degree of linear polarization of this combined beam using a rotating polarizer. We obtain the searched distribution P by changing the parameters of the reference beam – its intensity and state of polarization. This series of measurements allows to build the system of equations The values of the function P at various points P(θ i, ϕ j) are the searched variables of this system. Accuracy of that solution depends on how many measurements are done.
In this paper the authors present the idea for reconstructing one-photon states. Reconstructing a quantum state means measuring the probability distribution P that allows one to write the density operator for the analysed state. The most commonly known approach for the quantum reconstruction is the quantum tomography. Our alternative method assumes that the analysed field is coupled with the reference field which is described by the parameters settled during a measurement. In the proposed gedankenexperiment the degree of linear polarisation (DOLP) of this combined beam is measured using a rotating linear polariser. We state that it is possible to obtain the P-function by changing the parameters of reference beams and by preparing the series of DOLP measurements. This series of data leads to the system of equations. The values of the P-function at chosen points are the unknowns of this system. This article focuses on the numerical algorithm for solving these equations.
Abstract In this paper the authors discuss an alternative way for reconstructing one-photon mixed states of a partially polarized optical field. The task is to represent the probability density distribution describing these kind of states with the Stokes parameters which also characterize the effective state of polarization. These parameters can be measured by means of the degree of polarization with an experimental setup containing a rotating linear polarizer and a circular polarizer. A thought experiment is presented which assumes that the measurement is undertaken on an analyzed beam coupled with a reference beam containing photons polarized in a well-known way. The method discussed in the paper is an alternative for the most commonly used quantum tomography approach.
In this paper we discuss the reconstruction process of one-photon mixed states of partially polarised light. To solve this issue, we obtain the Stokes parameters by means of the degree of polarisation. The density operator describing the examined state is represented with these parameters. In the proposed two-beams method the degree of polarisation is measured on the analysed beam combined with reference beams containing photons with a settled state of polarisation. Coupling these beams allows one to obtain the Stokes parameters from the intensity contrast behind the rotating polariser. We discuss the influence of the quantum uncertainty on this technique of one-photon states reconstruction and we consider it for three aspects – the possibility of reducing the number of reference beams that are needed, the optimal state of polarisation of reference beams and the accuracy of the reconstruction method.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, thus finding excellent agreement.