Heisenberg scaling precision in multi-mode distributed quantum metrology

Abstract

We propose an $N$-photon Gaussian measurement scheme which allows the estimation of a parameter $\phi$ encoded into a multi-port interferometer with a Heisenberg scaling precision (i.e. of order $1/N$). In this protocol, no restrictions on the structure of the interferometer are imposed other than linearity and passivity, allowing the parameter $\phi$ to be distributed over several components. In all previous proposals Heisenberg scaling has been obtained provided that both the input state and the measurement at the output are suitably adapted to the unknown parameter $\phi$. This is a serious drawback which would require in practice the use of iterative procedures with a sequence of trial input states and measurements, which involve an unquantified use of additional resources. Remarkably, we find that only one stage has to be adapted, which leaves the choice of the other stage completely arbitrary. We also show that our scheme is robust against imperfections in the optimized stage. Moreover, we show that the adaptive procedure only requires a preliminary classical knowledge (i.e to a precision $1/\sqrt{N}$) on the parameter, and no further additional resources. As a consequence, the same adapted stage can be employed to monitor with Heisenberg-limited precision any variation of the parameter of the order of $1/\sqrt{N}$ without any further adaptation.

arXiv comment5 pages, 3 figures

References in corpus (28)

• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
• Continuous-variable optical quantum state tomography
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Distributed quantum sensing in a continuous variable entangled network
• A Geometric Perspective on Quantum Parameter Estimation
• Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement
• Distributed Quantum Metrology and the Entangling Power of Linear Networks
• Quantum optical technologies for metrology, sensing and imaging
• Optimal quantum-enhanced interferometry using a laser power source
• Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
• Optimal phase measurements with pure Gaussian states
• Thermally-Reconfigurable Quantum Photonic Circuits at Telecom Wavelength by Femtosecond Laser Micromachining
• Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control
• Collisional quantum thermometry
• Phase estimation for thermal Gaussian states
• $\pi$-Corrected Heisenberg Limit
• Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology
• Quantum-limited loss sensing: Multiparameter estimation and Bures distance between loss channels
• Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
• Bayesian estimation in homodyne interferometry
• Distributed Quantum Metrology with a Single Squeezed-Vacuum Source
• Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit
• Lattice quantum magnetometry
• Quantum magnetometry using two-stroke thermal machines
• Typicality of Heisenberg scaling precision in multi-mode quantum metrology

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• Heisenberg scaling precision in the estimation of functions of parameters
• Entanglement Enhanced Estimation of a Parameter Embedded in Multiple Phases
• Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements
• Heisenberg-scaling sensitivity in the estimation of two parameters in a Mach-Zehnder interferometer