Measuring the complete set of spatial Schmidt modes of entangled two-photon fields

TL;DR

This paper introduces a novel technique to measure the complete set of spatial Schmidt modes in entangled two-photon fields, enabling high-dimensional state characterization without prior knowledge, and reports the highest number of measured modes with high fidelity.

Contribution

The authors develop a method to directly measure the full set of spatial Schmidt modes in entangled photon pairs without prior basis information.

Findings

Measured over 3000 Schmidt modes, the highest reported to date.

Achieved up to 98% fidelity in mode measurement.

Demonstrated the technique's potential for high-dimensional quantum systems.

Abstract

Spontaneous parametric down-conversion (SPDC) is the most widely-used source of high-dimensional entangled two-photon states, and the entanglement in the spatial degree of freedom is considered best suited for harnessing high-dimensional advantages. Although the Schmidt basis provides a natural choice for state characterisation of entangled two-photon states in any degree of freedom, there is currently no technique that can measure the Schmidt basis of an entangled two-photon field. The existing techniques can only reconstruct the Schmidt spectrum when the Schmidt basis is known a priori. In contrast, we present a technique that measures the complete set of spatial Schmidt modes without any prior knowledge. Using this technique, we report measurement of states with over 3000 Schmidt modes -- highest reported yet -- with up to 98$\%$ fidelity. We expect our work to significantly advance the harnessing of high-dimensional advantages in SPDC-based systems.