Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

TL;DR

This paper derives a closed-form expression for the average fidelity of quantum rotosensors using anticoherent states, identifying optimal states for detecting rotations about unknown axes across various spin quantum numbers.

Contribution

It provides a general formula linking anticoherence measures to the optimal detection of rotations for arbitrary spin values, extending previous results.

Findings

Closed-form expression for average fidelity in terms of anticoherent measures

Identification of optimal rotosensors for spins up to j=7/2 and small angles up to j=5

Explanation of anticoherence measures' role in rotation detection

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.