At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
By M. Rams, P. Sierant, O. Dutta, Pawel Horodecki, J. Zakrzewski. 2017
147 citations recorded by the source corpus.
We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian the precision of its estimation is known to scale at most as $N^{-1}$ (Heisenberg scaling) in terms of the number of elementary subsystems used, $N$. The second approach considers fidelity at criticality often leading to an apparent super-Heisenberg scaling. However, scaling of time needed to ensure adiabaticity of the evolution brings back the the Heisenberg limit. We illustrate the general theory on a ferromagnetic Heisenberg spin chain which exhibits such super-Heisenberg scaling of fidelity around the critical value of the magnetic field. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the $N^{-1.5}$ scaling. In this case Fisher information sets the ultimate scaling as $N^{-1.75}$ which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultra-cold bosons in periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when time needed for preparation of quantum states involved is taken into acocunt.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/90eec1d1f5090376a0e8516bb052564705275278
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Quantum Fisher information matrix and multiparameter estimation (2019, background): “On the other hand, the enhancement of QFIM at the critical point indicates that the precision limit of the parameter can be improved near the phase transition, as shown in references [67,68].”