Positivity Conditions for the Density Matrix of Spin-One Particles

Pierre Minnaert

Received 17 February 1966DOI:https://doi.org/10.1103/PhysRevLett.16.672©1966 American Physical Society

Anton Vladimirovich Zabrodin, Alexander A. Ovchinnikov

W. Konar

X. Artru

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.

Volker Bach, Hans Konrad Knörr, Edmund Menge

Representability conditions on the one-and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals.A positivity condition for a certain kind of Grassmann integral is established which by an appropriate choice of the integrand, in turn, induces the well-known G-, P-and Q-Conditions of quantum chemistry.Similarly, the T 1 -and T 2 -Conditions are derived.Furthermore, quasifree Grassmann states are introduced and, for every operator γ ∈ H ⊕ H with 0 ≤ γ ≤ 1, the existence of a unique quasifree Grassmann state whose one-particle density matrix is γ is shown.. More specifically, ifwhere

Gergely Gidofalvi, David A. Mazziotti