Measurement strategy for spatially encoded photonic qubits

TL;DR

This paper introduces a probabilistic measurement strategy for spatially encoded photonic qubits that simplifies implementation and extends to high-dimensional systems, enhancing quantum information processing capabilities.

Contribution

It presents a new measurement scheme using a two-outcome POVM and fixed-position detection, avoiding displacement and enabling broader applications in quantum optics.

Findings

Probabilistic measurement reproduces observable statistics.

Compatible with current programmable liquid-crystal display technology.

Extensible to high-dimensional qudits and quantum information protocols.

Abstract

We propose a measurement strategy which can, probabilistically, reproduce the statistics of any observable for spatially encoded photonic qubits. It comprises the implementation of a two-outcome positive operator-valued measure followed by a detection in a fixed transverse position, making the displacement of the detection system unnecessary, unlike previous methods. This strategy generalizes a scheme recently demonstrated by one of us and co-workers restricted to measurement of observables with equatorial eigenvectors only. The method presented here can be implemented with the current technology of programmable multipixel liquid-crystal displays. In addition, it can be straightforwardly extended to high-dimensional qudits and may be a valuable tool in optical implementations of quantum information protocols with spatial qubits and qudits.