Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases

Year: 2017

Authors: Pezzč L., Ciampini MA., Spagnolo N., Humphreys PC., Datta A., Walmsley IA., Barbieri M., Sciarrino F., Smerzi A.

Autors Affiliation: CNR, INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Sapienza Univ Roma, Dipartimento Fis, Piazzale Aldo Moro 5, I-00185 Rome, Italy; Univ Oxford, Dept Phys, Clarendon Lab, Oxford OX1 3PU, England; Univ Warwick, Dept Phys, Coventry CV4 7AL, W Midlands, England; Univ Roma Tre, Dipartimento Sci, Via Vasca Navale 84, I-00146 Rome, Italy.

Abstract: A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 119 (13)      Pages from: 130504-1  to: 130504-6

More Information: M. B. is supported by a Rita Levi-Montalcini fellowship of Ministero dell’Istruzioni, dell’Universita e della Ricerca (MIUR). This work was supported by the European Research Council (ERC) Starting Grant 3DQUEST (3D-Quantum Integrated Optical Simulation; Grant Agreement No. 307783) and by the Horizon 2020 H2020-FETPROACT-2014 Grant QUCHIP (Quantum Simulation on a Photonic Chip; Grant Agreement No. 641039). A. D. is supported by the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom (EP/K04057X/2) and the United Kingdom National Quantum Technologies Program (EP/M01326X/1 and EP/M013243/1).
KeyWords: Interference; Entanglement; Limit
DOI: 10.1103/PhysRevLett.119.130504

Citations: 129
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