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/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.
Highlights
In quantum metrology one studies the resolution gains that can be attained when using quantum effects in the estimation strategy
While squeezing has been used in quantum metrology for specific systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14], there is no general theory of squeezing-based metrology that holds for arbitrary measurements and systems
The main result of this paper is a unified framework that describes all previous metrology protocols that use squeezing in any quantum system and any observable, as it is based on the elegant general theory of squeezing for arbitrary systems [27]
Summary
In quantum metrology one studies the resolution gains that can be attained when using quantum effects in the estimation strategy. The usual setting considers an estimation strategy where a parameter φ is encoded onto a probe state through a unitary transformation Uφ = eiHφ, where H is the probe Hamiltonian. The main result of this paper is a unified framework that describes all previous (and presumably future) metrology protocols that use squeezing in any quantum system and any observable, as it is based on the elegant general theory of squeezing for arbitrary systems [27]. As in entanglement-based quantum metrology, a quadratic resolution gain is obtained in this case, if one compares the resolution attainable with a squeezed probe to the resolution obtainable with N classical probes (i.e. prepared in a coherent state) of total energy E, Fig. 1b. We conclude with a step-by-step procedure to obtain new squeezing based metrology protocols
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