Numerical reconstruction of one-photon mixed states by means of the degree of linear polarisation

Abstract

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.

Keywords:

• photons
• degree of linear polarisation
• quantum state reconstruction
• numerical algorithm