Casimir Invariants for Systems Undergoing Collective Motion

TL;DR

This paper introduces a general method for calculating invariants in systems of particles undergoing collective motion, aiding in identifying observables and logical operations for decoherence-free subsystems, including particles with multiple internal states.

Contribution

The paper presents a novel, general approach to compute invariants for collective particle systems, extending to particles with more than two internal states, useful for quantum information processing.

Findings

Provides a method to determine complete sets of commuting observables.

Identifies logical operations for decoherence-free/noiseless subsystems.

Applicable to systems with particles having multiple internal states.

Abstract

Dicke states are states of a collection of particles which have been under active investigation for several reasons. One reason is that the decay rates of these states can be quite different from a set of independently evolving particles. Another reason is that a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, can avoid certain types of errors in quantum information processing devices. Here we provide a method for calculating invariants of systems of particles undergoing collective motions. These invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as identify possible logical operations for decoherence-free/noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.