Perfect quantum protractors
- URL: http://arxiv.org/abs/2310.13045v1
- Date: Thu, 19 Oct 2023 18:00:01 GMT
- Title: Perfect quantum protractors
- Authors: Micha{\l} Piotrak, Marek Kopciuch, Arash Dezhang Fard, Magdalena
Smolis, Szymon Pustelny, Kamil Korzekwa
- Abstract summary: Perfect quantum protractors can only exist for systems with a well-defined total angular momentum $j$.
Perfect quantum protractors form an optimal resource for a metrological task of estimating the angle of rotation around.
- Score: 0.873811641236639
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper we introduce and investigate the concept of a perfect quantum
protractor, a pure quantum state $|\psi\rangle\in\mathcal{H}$ that generates
three different orthogonal bases of $\mathcal{H}$ under rotations around each
of the three perpendicular axes. Such states can be understood as pure states
of maximal uncertainty with regards to the three components of the angular
momentum operator, as we prove that they maximise various entropic and
variance-based measures of such uncertainty. We argue that perfect quantum
protractors can only exist for systems with a well-defined total angular
momentum $j$, and we prove that they do not exist for $j\in\{1/2,2,5/2\}$, but
they do exist for $j\in\{1,3/2,3\}$ (with numerical evidence for their
existence when $j=7/2$). We also explain that perfect quantum protractors form
an optimal resource for a metrological task of estimating the angle of rotation
around (or the strength of magnetic field along) one of the three perpendicular
axes, when the axis is not $\textit{a priori}$ known. Finally, we demonstrate
this metrological utility by performing an experiment with warm atomic vapours
of rubidium-87, where we prepare a perfect quantum protractor for a spin-1
system, let it precess around $x$, $y$ or $z$ axis, and then employ it to
optimally estimate the rotation angle.
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