Truncated su(2) moment problem for spin and polarization states

Abstract

We address the problem whether a given set of expectation values is compatible with the first and second moments of the generic spin operators of a system with total spin j. Those operators appear as the Stokes operator in quantum optics, as well as the total angular momentum operators in the atomic ensemble literature. We link this problem to a particular extension problem for bipartite qubit states; this problem is closely related to the symmetric extension problem that has recently drawn much attention in different contexts of the quantum information literature. We are able to provide operational, approximate solutions for every large spin numbers, and in fact the solution becomes exact in the limiting case of infinite spin numbers. Solutions for low spin numbers are formulated in terms of a hyperplane characterization, similar to entanglement witnesses, that can be efficiently solved with semidefinite programming.

18 pages, 1 figure

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• Spin squeezing and entanglement
• Testing nonclassicality in multimode fields: a unified derivation of classical inequalities
• Entanglement and permutational symmetry
• Spin squeezing inequalities for arbitrary spin
• Spin squeezing and entanglement for arbitrary spin
• Separability criteria and entanglement witnesses for symmetric quantum states
• Entanglement verification with realistic measurement devices via squashing operations
• Certifying experimental errors in quantum experiments
• Iterations of nonlinear entanglement witnesses
• Analysing multiparticle quantum states