Units of rotational information

TL;DR

This paper introduces the concept of Cartesian refbits as elementary units of rotational information, demonstrating reversible conversions of spin-J Bell states into spin-1/2 Bell states and linking state conversion fidelity to gate simulation accuracy.

Contribution

It establishes a foundational framework for quantifying and converting rotational quantum resources, including the definition of Cartesian refbits and methods for approximate state and gate conversions.

Findings

Reversible conversion of spin-J Bell states into spin-1/2 Bell states at a rate determined by quantum Fisher information.

Design of machines for approximate conversion between higher-spin Bell states and Cartesian refbits.

Quantitative bounds linking state conversion fidelity to the accuracy of unitary gate simulation.

Abstract

Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.