Classical positivity, quantum positivity and entanglement of a multi-partite density matrix, with the example of polarized reactions

摘要

The spin correlations in a reaction involving initial and final polarized particles are encoded in a cross section matrix which is taken as an example of multipartite density matrix. Quantum positivity stipulates that the cross section is positive for any spin states - separable or entangled - of the particles. A weaker condition, classical positivity only requires that the cross section is positive for separable spin state. Classical and Quantum positivity are represented by diagrams. The domains of classical positivity and of separability are dual under a reciprocal polar transformation. This property can be usefull in quantum information theory.