Squeezing metrology: a unified framework

Lorenzo Maccone and Alberto Riccardi

Dip. Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy

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Abstract

Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among $N$ probes. Typically, a quadratic gain in resolution is achievable, going from the $1/\sqrt{N}$ of the central limit theorem to the $1/N$ of the Heisenberg bound. Here we focus instead on quantum squeezing and provide a unified framework for metrology with squeezing, showing that, similarly, one can generally attain a quadratic gain when comparing the resolution achievable by a squeezed probe to the best $N$-probe classical strategy achievable with the same energy. Namely, here we give a quantification of the Heisenberg squeezing bound for arbitrary estimation strategies that employ squeezing. Our theory recovers known results (e.g. in quantum optics and spin squeezing), but it uses the general theory of squeezing and holds for arbitrary quantum systems.

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[1] H.P. Yuen, Contractive States and the Standard Quantum Limit for Monitoring Free-Mass Positions, Phys. Rev. Lett. 51, 719 (1983).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.51.719

[2] H.P. Yuen, Two-photon coherent states of the radiation field, Phys. Rev. A 13, 2226 (1976).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.13.2226

[3] A. Perelomov, Generalized coherent states and their applications (Springer, 1986).
https:/​/​doi.org/​doi:10.1007/​978-3-642-61629-7

[4] M. Ozawa, Measurement breaking the standard quantum limit for free-mass position, Phys. Rev. Lett. 60, 385 (1988).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.60.385

[5] D.A. Trifonov, Generalized uncertainty relations and coherent and squeezed states, JOSA A 17, 2486 (2000).
https:/​/​doi.org/​doi:10.1364/​JOSAA.17.002486

[6] C. Aragone, E. Chalbaud, and S. Salamó, On intelligent spin states, J. Math. Phys. 17, 1963 (1976).
https:/​/​doi.org/​doi:10.1063/​1.522835

[7] D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A 46, R6797 (1992).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.46.R6797

[8] M. Kitagawa, M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.47.5138

[9] D. J. Wineland, J. J. Bollinger, W. M. Itano, D. J. Heinzen, Squeezed atomic states and projection noise in spectroscopy, Phys. Rev. A 50, 67 (1994).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.50.67

[10] J. Ma, X. Wang, C. P. Sun, F. Nori, Quantum spin squeezing, Phys. Rep. 509, 89 (2011).
https:/​/​doi.org/​doi:10.1016/​j.physrep.2011.08.003

[11] A. Luis, J. Peřina, SU(2) coherent states in parametric down-conversion, Phys. Rev. A 53, 1886 (1996).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.53.1886

[12] C. Brif, A. Mann, Nonclassical interferometry with intelligent light, Phys. Rev. A 54, 4505 (1996).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.54.4505

[13] A.I. Lvovsky, Squeezed light, in Photonics Volume 1: Fundamentals of Photonics and Physics, pg. 121 (Wiley, 2015). arXiv:1401.4118v2.
arXiv:1401.4118v2

[14] J. Flórez, E. Giese, D. Curic, L. Giner, R.W. Boyd, J.S. Lundeen, The phase sensitivity of a fully quantum three-mode nonlinear interferometer, New J. Phys. 20, 123022 (2018).
https:/​/​doi.org/​doi:10.1088/​1367-2630/​aaf3d2

[15] B.E. Anderson, B.L. Schmittberger, P. Gupta, K.M. Jones, P.D. Lett, Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers, Phys. Rev. A 95, 063843 (2017).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.95.063843

[16] V. Giovannetti, S. Lloyd, L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.96.010401

[17] S. L. Braunstein, C. M. Caves, G. J. Milburn, Generalized uncertainty relations: Theory, examples, and Lorentz invariance, Ann. Phys. 247, 135-173 (1996).
https:/​/​doi.org/​doi:10.1006/​aphy.1996.0040

[18] S. L. Braunstein, C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.72.3439

[19] M. Zwierz, C. A. Pérez-Delgado, P. Kok, Ultimate limits to quantum metrology and the meaning of the Heisenberg limit, Phys. Rev. A 85, 042112 (2012).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.85.042112

[20] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit, Science 306, 1330 (2004).
https:/​/​doi.org/​doi:10.1126/​science.1104149

[21] V. Giovannetti, S. Lloyd, L. Maccone, Advances in quantum metrology, Nature Phot. 5, 222 (2011).
https:/​/​doi.org/​doi:10.1038/​nphoton.2011.35

[22] M. G. A. Paris, Quantum estimation for quantum technology, Int. J. Quantum Inf. 7, 125 (2009).
https:/​/​doi.org/​doi:10.1142/​S0219749909004839

[23] R. Demkowicz-Dobrzański, M. Jarzyna, J. Kołodyński, Quantum Limits in Optical Interferometry, Progress in Optics, 60, 345 (2015).
https:/​/​doi.org/​doi:10.1016/​bs.po.2015.02.003

[24] G. Tóth, I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A: Math Th. 47, 424006 (2014).
https:/​/​doi.org/​doi:10.1088/​1751-8113/​47/​42/​424006

[25] M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, I. A. Walmsley, Experimental quantum-enhanced estimation of a lossy phase shift, Nature Photonics 4, 357 (2010).
https:/​/​doi.org/​doi:10.1038/​nphoton.2010.39

[26] D.S. Simon, G. Jaeger, A.V. Sergienko, Quantum Metrology, Imaging, and Communication (Springer, 2017).
https:/​/​doi.org/​10.1007/​978-3-319-46551-7

[27] J. C. F. Matthews, et al. Towards practical quantum metrology with photon counting, NPJ Quantum Inf. 2, 16023 (2016).
https:/​/​doi.org/​doi:10.1038/​npjqi.2016.23

[28] D.A. Trifonov, Generalized intelligent states and squeezing, J. Math. Phys. 35, 2297 (1994).
https:/​/​doi.org/​doi:10.1063/​1.530553

[29] H.P. Robertson, The uncertainty principle, Phys. Rev. 34, 163 (1929).
https:/​/​doi.org/​doi:10.1103/​PhysRev.34.163

[30] V. Giovannetti, S. Lloyd, L.Maccone, Quantum measurement bounds beyond the uncertainty relations, Phys. Rev. Lett. 108, 260405 (2012).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.108.260405

[31] N. Margolus, L. B. Levitin, The maximum speed of dynamical evolution, Physica D 120, 188 (1998).
https:/​/​doi.org/​doi:10.1016/​S0167-2789(98)00054-2

[32] L. Mandelstam, I. G. Tamm, The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics, J. Phys. USSR 9, 249 (1945).
https:/​/​doi.org/​doi:10.1007/​978-3-642-74626-0_8

[33] A. Peres, Quantum Theory: Concepts and Methods, (Kluwer ac. publ., Dordrecht, 1993).

[34] R. Demkowicz-Dobrzański, J. Kołodyński, M. Guţă, The elusive Heisenberg limit in quantum-enhanced metrology, Nature Comm. 3, 1063 (2012).
https:/​/​doi.org/​doi:10.1038/​ncomms2067

[35] B. M. Escher, R. L. de Matos Filho, L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Phys. 7, 406 (2011).
https:/​/​doi.org/​10.1038/​nphys1958

[36] S.M. Barnett D.T. Pegg, On the Hermitian Optical Phase Operator, J. Mod. Opt. 36, 7 (1988).
https:/​/​doi.org/​%20doi:10.1080/​09500348914550021

[37] A.S. Holevo, Probabilistic and Statistical Aspect of Quantum Theory (Edizioni della Normale, Pisa 2011, reprinted from 1980).

[38] P. Carruthers M.M. Nieto, Phase and Angle Variables in Quantum Mechanics, Rev. Mod. Phys. 40, 411 (1968).
https:/​/​doi.org/​doi:10.1103/​RevModPhys.40.411

[39] R. Jackiw, Minimum Uncertainty Product, Number-Phase Uncertainty Product, and Coherent States, J. Math. Phys. 9, 339 (1968).
https:/​/​doi.org/​doi:10.1063/​1.1664585

[40] Y. Yamamoto, N. Imoto, and S. Machida, Amplitude squeezing in a semiconductor laser using quantum nondemolition measurement and negative feedback, Phys. Rev. A 33, 3243 (1986).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.33.3243

[41] A.D. Wilson-Gordon, V. Buek, P.L. Knight, Statistical and phase properties of displaced Kerr states, Phys. Rev. A 44, 7647 (1991).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.44.7647

[42] C.M. Caves, Quantum-mechanical noise in an interferometer, Phys. Rev. D 23, 1693 (1981).
https:/​/​doi.org/​doi:10.1103/​PhysRevD.23.1693

[43] L. Pezzé, A. Smerzi, Mach-Zehnder Interferometry at the Heisenberg Limit with Coherent and Squeezed-Vacuum Light, Phys. Rev. Lett. 100, 073601 (2008).
https:/​/​doi.org/​doi:10.1103/​PhysRevLett.100.073601

[44] S. Lloyd, private communication (2010).

[45] C.M.A. Dantas, N.G. de Almeida, B. Baseia, Statistical Properties of the Squeezed Displaced. Number States, Braz. J. Phys. 28, 462 (1998).
https:/​/​doi.org/​doi:10.1590/​S0103-97331998000400021

[46] T. Matsubara, P. Facchi, V. Giovannetti, K. Yuasa, Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit, New J. Phys. 21, 033014 (2019).
https:/​/​doi.org/​doi:10.1088/​1367-2630/​ab0604

[47] A. De Pasquale, P. Facchi, G. Florio, V. Giovannetti, K. Matsuoka, K. Yuasa, Two-mode bosonic quantum metrology with number fluctuations, Phys. Rev. A 92, 042115 (2015).
https:/​/​doi.org/​doi:10.1103/​PhysRevA.92.042115

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