Experimental optical phase measurement approaching the exact Heisenberg limit

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.

(12 pages, 6 figures), typos corrected

References in corpus (4)

• Beating the Standard Quantum Limit with Four Entangled Photons
• Entanglement-free Heisenberg-limited phase estimation
• Entanglement-enhanced measurement of a completely unknown phase
• Unconditional violation of the shot noise limit in photonic quantum metrology

Cited by in corpus (45)

• Photonic quantum information processing: a concise review
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Distributed quantum phase estimation with entangled photons
• Quantum computing with rotation-symmetric bosonic codes
• Learning Quantum Systems
• Tutorial: Optical quantum metrology
• $\pi$-Corrected Heisenberg Limit
• Quantum-enhanced interferometry with large heralded photon-number states
• Field demonstration of distributed quantum sensing without post-selection
• Deterministic quantum phase estimation beyond the ideal NOON state limit
• Non-Markovian Sensing of a Quantum Reservoir
• Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology
• Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
• Bayesian Quantum Multiphase Estimation Algorithm
• Experimental multiparameter quantum metrology in adaptive regime
• Digital Discovery of 100 diverse Quantum Experiments with PyTheus
• Information geometry under hierarchical quantum measurement
• Non-asymptotic Heisenberg scaling: experimental metrology for a wide resources range
• Benchmarking Machine Learning Algorithms for Adaptive Quantum Phase Estimation with Noisy Intermediate-Scale Quantum Sensors
• Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
• Threshold for a discrete-variable sensor of quantum reservoirs
• Optical Phase Measurement Using a Deterministic Source of Entangled Multi-photon States
• Squeezing phase diffusion
• Beating the classical phase precision limit using a quantum neuromorphic platform
• Single-shot non-Gaussian Measurements for Optical Phase Estimation
• Quantum Polarimetry
• Experimental investigation of Bayesian bounds in multiparameter estimation
• Determination of the asymptotic limits of adaptive photon counting measurements for coherent-state optical phase estimation
• Verifying the security of a continuous variable quantum communication protocol via quantum metrology
• Optimizing quantum-enhanced Bayesian multiparameter estimation of phase and noise in practical sensors
• Phase estimation algorithm for the multibeam optical metrology
• Using Schroedinger cat quantum state for detection of a given phase shift
• Single-shot Quantum Signal Processing Interferometry
• Enhancing Quantum Metrology by Quantum Resonance Dynamics
• Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound
• Relative Phase Distribution and the Precision of Optical Phase Sensing in Quantum Metrology
• Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction
• Bures geodesics and quantum metrology
• Experimental investigation of a multi-photon Heisenberg-limited interferometric scheme: the effect of imperfections
• Modal complexity as a metric for Anderson localization
• Advantages of one and two-photon inverse scattering
• Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements
• Probing parameters estimation with Gaussian non-commutative measurements
• Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements
• Adaptive Bayesian algorithm for achieving desired quantum transition