Phase-space measurements and decoherence for angular momentum systems

TL;DR

This paper compares two models of quantum decoherence in angular momentum systems, revealing subtle differences in their dynamics and implications for classicality characterization.

Contribution

It introduces and contrasts two decoherence models for angular momentum systems, highlighting their non-equivalence and impact on phase-space and classicality.

Findings

The two models' super-operators are commutative but have different eigenvalues.

Both models induce phase-space decoherence but exhibit distinct dynamical behaviors.

Decoherence and classicality criteria are not equivalent in angular momentum systems.

Abstract

The monitoring of the three independent components of the angular momentum (or spin) of a quantum system by its environment that does not isolate any preferred orientation is modelled in two different ways. One describes the dynamics by the Lindblad equation generated by three independent angular momentum operators. The other uses iterated measurements of the ``phase-space'' point on the sphere in terms of the positive operator-valued measure generated by SU(2) coherent states. In contrast to the equivalent scenario on a flat phase space, these two models give rise to subtle differences. Specifically, it is shown that the two super-operators corresponding to the two decoherence models for angular momentum systems are commutative, but their eigenvalues are different. Hence although both models give rise to phase-space decoherence, their dynamical behaviours are not equivalent. In either model, we find that the characterisation of classicality as represented by the decay rates of the elements of the density matrix (i.e. decoherence) and that as represented by the positivity of the quasiprobability distribution are not equivalent for angular momentum systems.