Three-photon polarization ququarts: polarization, entanglement and Schmidt decompositions

Abstract

We consider polarization states of three photons, each in the same given spectral-angular mode. A general form of such states is a superposition of four basic three-photon polarization modes, to be referred to as three-photon polarization ququarts. All such states can be considered as consisting of one-and two-photon parts, which can be entangled with each other. The degrees of entanglement and polarization as well as the Schmidt decomposition and Stokes vectors of three-photon polarization ququarts are found and discussed.

Analysis of quantum tomography protocol efficiency for triphoton polarization states

“…It acts as a measure of information about parameters of a quantum state contained in the measurements determined by the tomography protocol. Above we have described complete tomographic protocols, i.e., protocols that provide arbitrarily accurate recovery of any mixed state as the sample size grows 28 .…”

“…All possible superpositions of states (9) span a state space of a three-photon polarization ququart 28…”

“…States such as HHV , HVH и VHH are not distinguishable and the overall quantum state is described by a vector in a four dimensional space. Such states are described as triphoton polarization ququart 28 .…”

“…All possible superpositions of states ( 9) span a state space of a three-photon polarization ququart 28 . Vector columns of previously described states form the matrix G that performs the transition from the four-dimensional basis to original eight-dimensional one.…”

Luminescence in germania–silica fibers in a 1–2 μm region

“…Thus the development an effective three-photon source can become the next big step in this progress. Generation of GHZ-states [37], study the features of three-photon polarization states [11], heralded generation of entangled biphotons are possible applications of such three-photon source.…”