Shannon dimensionality of quantum channels and its application to photon entanglement

TL;DR

This paper introduces Shannon dimensionality as a new experimental measure of bipartite entanglement, demonstrated through orbital-angular-momentum entangled photons, with potential for high-dimensional quantum information applications.

Contribution

It proposes a novel measure of entanglement called Shannon dimensionality and demonstrates its practical application in quantifying photon entanglement experimentally.

Findings

Shannon dimensionality D varies between 2 and 6 in experiments.

D can be predicted to increase with more angular sectors in the phase plate.

D=50 is predicted to be achievable in future experiments.

Abstract

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens-coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D = 50 is experimentally within reach.