Universal linear optical operations on discrete phase-coherent spatial modes

TL;DR

This paper presents a scalable, high-fidelity method for implementing arbitrary linear optical operations on high-dimensional spatial modes using phase gratings on spatial light modulators, advancing quantum and classical optical processing.

Contribution

The authors introduce a non-cascaded, versatile approach for performing high-dimensional linear operations with high fidelity, surpassing previous methods in dimensionality and applicability.

Findings

Achieved unitary transformations for 7 to 24 dimensions with fidelities from 95.1% to 82.1%.

Demonstrated non-unitary operator for quantum state tomography with 94.9% fidelity.

Method is adaptable to various devices beyond SLMs.

Abstract

Linear optical operations are fundamental and significant for both quantum mechanics and classical technologies. We demonstrate a non-cascaded approach to perform arbitrary unitary and non-unitary linear operations for N-dimensional phase-coherent spatial modes with meticulously designed phase gratings. As implemented on spatial light modulators (SLMs), the unitary transformation matrix has been realized with dimensionalities ranging from 7 to 24 and the corresponding fidelities are from 95.1% to 82.1%. For the non-unitary operators, a matrix is presented for the tomography of a 4-level quantum system with a fidelity of 94.9%. Thus, the linear operator has been successfully implemented with much higher dimensionality than that in previous reports. It should be mentioned that our method is not limited to SLMs and can be easily applied on other devices. Thus we believe that our proposal provides another option to perform linear operation with a simple, fixed, error-tolerant and scalable scheme.