Quantum-limited Euler angle measurements using anticoherent states

TL;DR

This paper introduces anticoherent quantum states that enable measurement of Euler angles with sensitivities reaching the quantum limit, surpassing shot noise, and provides a geometric method to find such states for advanced quantum metrology.

Contribution

It derives a quantum Cramér-Rao bound for multiparameter rotation estimation and identifies anticoherent states as optimal for Heisenberg-limited sensitivities.

Findings

Anticoherent states achieve Heisenberg-limited sensitivities for all rotation parameters.

A geometric technique for discovering new anticoherent states is developed.

The quantum Cramér-Rao bound for multiparameter rotation estimation is established.

Abstract

Many protocols require precise rotation measurement. Here we present a general class of states that surpass the shot noise limit for measuring rotation around arbitrary axes. We then derive a quantum Cram\'er-Rao bound for simultaneously estimating all three parameters of a rotation (e.g., the Euler angles), and discuss states that achieve Heisenberg-limited sensitivities for all parameters; the bound is saturated by "anticoherent" states [Zimba, Electron. J. Theor. Phys. 3, 143 (2006)] (we are reluctant to use "anticoherent" to describe the states, but the name has become commonplace over the last decade). Anticoherent states have garnered much attention in recent years, and we elucidate a geometrical technique for finding new examples of such states. Finally, we discuss the potential for divergences in multiparameter estimation due to singularities in spherical coordinate systems. Our results are useful for a variety of quantum metrology and quantum communication applications.