Optimal simultaneous measurements of incompatible observables of a single photon

TL;DR

This paper experimentally demonstrates the optimal joint measurement of incompatible qubit observables using a minimal-resource optical setup, confirming fundamental tradeoff relations with high quantum-limited performance.

Contribution

It provides the first optical implementation of a minimal-resource optimal joint measurement for qubits, directly testing a fundamental tradeoff relation.

Findings

Confirmed the tradeoff relation for measurement sharpness.

Achieved quantum-limited performance with a heralded single-photon source.

Demonstrated the simplest possible optimal joint measurement scheme.

Abstract

Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with corresponding different tradeoff relations for the measurements. Understanding the limitations of such measurements is of fundamental interest and relevant for quantum technology. Here, we experimentally test a tradeoff relation for the sharpness of qubit measurements, a relation which refers directly to the form of the measurement operators, rather than to errors in estimates. We perform the first optical implementation of the simplest possible optimal joint measurement, requiring less quantum resources than have previously often been employed. Using a heralded single-photon source, we demonstrate quantum-limited performance of the scheme on single quanta.