Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
1Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, University of Liège, B-4000 Liège, Belgium
2Department of Mathematics, University of York, UK-York YO10 5DD, United Kingdom
3Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
Published: | 2020-06-22, volume 4, page 285 |
Eprint: | arXiv:1909.08355v2 |
Doi: | https://doi.org/10.22331/q-2020-06-22-285 |
Citation: | Quantum 4, 285 (2020). |
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Abstract
Coherent and anticoherent states of spin systems up to spin $j=2$ are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number $j$. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to $j=7/2$ and (ii) for small rotation angles in the case of spin quantum numbers up to $j=5$. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of $j$.

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