# 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

### 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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### Cited by

[1] Giovanni Gramegna, Danilo Triggiani, Paolo Facchi, Frank A. Narducci, and Vincenzo Tamma, "Typicality of Heisenberg scaling precision in multimode quantum metrology", Physical Review Research 3 1, 013152 (2021).

[2] Emanuele Polino, Mauro Valeri, Nicolò Spagnolo, and Fabio Sciarrino, "Photonic quantum metrology", AVS Quantum Science 2 2, 024703 (2020).

[3] Stella Seah, Stefan Nimmrichter, Daniel Grimmer, Jader P. Santos, Valerio Scarani, and Gabriel T. Landi, "Collisional Quantum Thermometry", Physical Review Letters 123 18, 180602 (2019).

[4] Dario Gatto, Paolo Facchi, Frank A. Narducci, and Vincenzo Tamma, "Distributed quantum metrology with a single squeezed-vacuum source", Physical Review Research 1 3, 032024 (2019).

[5] Lorenzo Maccone and Changliang Ren, "Quantum Radar", Physical Review Letters 124 20, 200503 (2020).

[6] Sascha Wald, Saulo V. Moreira, and Fernando L. Semião, "In- and out-of-equilibrium quantum metrology with mean-field quantum criticality", Physical Review E 101 5, 052107 (2020).

[7] Giovanni Gramegna, Danilo Triggiani, Paolo Facchi, Frank A. Narducci, and Vincenzo Tamma, "Heisenberg scaling precision in multi-mode distributed quantum metrology", New Journal of Physics 23 5, 053002 (2021).

[8] Marco Genovese, "Experimental Quantum Enhanced Optical Interferometry", arXiv:2101.02891.

[9] Danilo Triggiani, Paolo Facchi, and Vincenzo Tamma, "Heisenberg scaling precision in the estimation of functions of parameters", arXiv:2103.08564.

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