Experimental optical phase measurement approaching the exact Heisenberg limit

TL;DR

This paper demonstrates a quantum optical phase measurement scheme that approaches the Heisenberg limit with near-optimal precision, surpassing previous methods and establishing a fundamental limit in quantum metrology.

Contribution

The authors present a novel experimental scheme combining entanglement, multiple phase sampling, and adaptive measurement to achieve true Heisenberg limit precision in optical phase estimation.

Findings

Achieved phase measurement within 4% of the Heisenberg limit.

Surpassed the best precision of simpler techniques with N=3 photon passes.

Demonstrated fundamental limits of quantum metrology with photonic qubits.

Abstract

The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement---the estimation of a completely unknown phase---has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able---even in principle---to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is $N=3$. We achieve a precision that is within $4\%$ of the HL, surpassing the best precision theoretically achievable with simpler techniques with $N=3$. This work represents a fundamental achievement of the ultimate limits of metrology, and the scheme can be extended to higher $N$ and other physical systems.