Classical and quantum constraints in spin physics

TL;DR

This paper explores classical and quantum constraints on spin observables in physics, highlighting how symmetries and positivity conditions differ between classical and quantum regimes, especially regarding entangled particles.

Contribution

It distinguishes classical from non-classical constraints on spin observables and reveals the duality between classical positivity domains and separability in quantum states.

Findings

Classical constraints ensure invariance of cross sections under symmetries.

Non-classical constraints apply at the amplitude level, involving entanglement.

Classical positivity domain is dual to the domain of separability.

Abstract

Constraints on spin observables coming from discrete symmetries such as P, C, T and identical particles may be divided in two types: 1) classical ones, which insure the invariance of the cross sections under the symmetry operation; 2) non-classical ones, which can only be obtained at the level of amplitudes. Similarly, positivity constraints can be divided into classical and non-classical constraints. The former insure the positivity of the cross section for arbitrary individual polarisations of the external particles, the latter extend this requirement to the case of entangled external spins. The domain of classical positivity is shown to be dual to the domain of separability