We experimentally investigate quantum polarization of three-photon states. A number of representative three-photon states are prepared and tested for quantum polarization properties. Our results reveal interesting properties like hidden polarization.
We experimentally investigate various quantum polarization features of three-photon quantum states, including product and entangled states with varying purity. The three-photon quantum states are categorized into six classes based on the rotation symmetry of mean, variance, and skewness of the polarization distribution. The representative three-photon quantum states in each category are prepared from double-pair emission from pulsed spontaneous parametric down-conversion and quantum interferometry. We demonstrate that the three-photon quantum states show interesting quantum polarization properties, such as maximum sum-uncertainty and hidden polarizations.
In quantum information processing, one of the most common methods to represent a qubit is by means of the polarization degree of freedom of a photon. Efficient methods to determine the photon polarization state are hence the fundamental tools in the studies of qubit systems. In fact, both theoretically optimal and practical polarization measurement schemes have been investigated extensively in the past two decades. These studies nevertheless focus on the situation when a definite number of photons are given and the results demonstrate the polarization estimation performance in terms of the mean fidelity [1, 2].
In this thesis, we experimentally test fundamental properties of quantum mechanics, namely \nnon-locality (in the form of three new families of Bell's inequalities) and the symmetry of \nenvariance. To accomplish these we use a Sagnac source of polarization entangled photon \npairs. \nIn chapters one and two we discuss the relevant background information in quantum \ninformation theory, nonlinear optics, experimental realization of polarization entangled \nphotons and a trouble-shooting and maintenance guide for a Saganc source. \nIn chapter three we experiment with a set of three newly derived families of Bell's \ninequalities. These three families are predicted to yield the largest volume of violation of \nthe local hidden variable models (LHVM). Our experimental results are in good agreement \nwith those predictions and therefore, represent the largest volume of experimental violation \nof LHVM to date. We showed a violation of up to 30 sigma from what is predicted by LHVM, \nand our results followed closely to the predictions of quantum mechanics. \nIn chapter four we experimentally test envariance, an assisted-symmetry exhibited by \nspecifi c quantum systems. Envariance is a fundamental property in the quantum world that \nhas lacked, until now, extensive experimental study. The symmetry has ramifi cations in the \nfoundations of quantum mechanics, and plays an integral role in a proof of Born's rule [1]. \nOur results serve as a benchmark the property of envariance. We show that experimental \nquantum states can be (99.66+/- 0.04)% envariant over a wide range of transformations, as \nmeasured using the average quantum fi delity [2], and (99.963 +/- 0.005)% as measured using \na modifi ed average Bhattacharya Coeffi cient [3], a measure of the overlap of two probability \ndistributions.
Quantum polarization properties of two-mode states have been discussed in the context of quantum states with ``hidden polarization''. In this paper we demonstrate that all pure two-photon and three-photon states have unit degree of quantum polarization. We also show that pure states belonging to groups of discrete symmetry have unit degree of quantum polarization for arbitrary number of photons. For a certain class of two-photon states, we substantiate the possibility of generating the full basis set (three orthogonal states) by using only combinations of the SU(2) generators, i.e., by using geometrical rotations and differential phase shifts. Finally, we generate the whole basis set for pure reflection-symmetrical three-photon states by means of SU(2) generators.