Experimental polarization state tomography using photon counting polarimeters

Abstract

We report on the implementation of a photon counting polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-1 2 quantum systems. We show how to use this polarimeter to estimate the complete polarization state for generic multi-photon states. State reconstruction using the polarimeter is illustrated by actual measurements on prepared ensembles of one-and two-photon systems. The rate at which the estimated polarization state converges to an asymptote state is also measured and presented.

Quantum state tomography with fully symmetric measurements and product measurements

“…In the case of a qubit, we compare the similarities and differences between SIC POM and MUB as well as other measurements constructed out of platonic solids. We also discuss in detail the dependence of the reconstruction error on the Bloch vector of the unknown true state and make a connection with the experimental data given by Ling et al [27].…”

“…Our study confirms that the result based on random-matrix theory is already quite accurate for d = 2, although it is best justified when d is large. As a simple application, we make contact with the experimental result given by Ling et al [27].…”

“…(24) and (27) shows that the value N 2 Tr[C(ρ) 2 ] for a SIC POM is roughly in the middle of the lower bound and the upper bound for tight IC measurements.…”

“…We then derive exact formulas for the mean trace distances for both isotropic measurements and SIC POM and explain the dependence of the reconstruction error on the Bloch vector of the true state (see Refs. [12,27,28] for earlier accounts). Our study confirms that the result based on random-matrix theory is already quite accurate for d = 2, although it is best justified when d is large.…”

“…However, little is known about the tomographic resources required to achieve a given accuracy as measured by the trace distance since its definition involves taking the square root of a positive operator. Even for the qubit SIC POM [12,27,28], no analytic formula is known concerning the mean trace distance between the estimator and the true state. One motivation of the present study is to solve this long-standing open problem.…”