Shannon dimensionality of quantum channels and its application to photon entanglement

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.

4 pages, 3 figures, accepted for Physical Review Letters

References in corpus (3)

• Testing the Hilbert space dimension
• On Secure Quantum Key Distribution Using Continuous Variables of Single Photons
• Schmidt number of pure bi-partite entangled states and methods of its calculation

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• Experimental demonstration of free-space information transfer using phase modulated orbital angular momentum radio
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• The physics of angular momentum radio
• A tight Tsirelson inequality for infinitely many outcomes
• Size invariant twisted optical modes for efficient generation of higher dimensional quantum states