Spin-entanglement in a three electron system produced in double Auger decay

Abstract

The simultaneous emission of two electrons in photoionization, or in the non-radiative spontaneous decay of an inner-shell vacancy, are two of the best known examples of the failure of the independent-particle model of atoms and molecules. The later of these provides also one of the two competitive processes, following inner-shell photoionization, for producing three flying electrons which can, for example, be used in implementing many protocols hitherto developed in quantum information. The correlation properties of the three-particle system consisting of these two electrons plus the photoelectron are analyzed using methods from quantum information theory. The entanglement of the consequent tripartite spin-state is shown to be completely independent of the mechanism(s) which may be responsible for the emission of these three electronic qubits in two different steps in the absence of spin-orbit interaction. Our analysis shows that the tripartite state formed in the present case is more like a |W〉 class of states possessing pairwise entanglement. The experimental characterization of these states is fully achieved merely by the measurements of the energies of three flying electrons, without requiring any entanglement witness or other similar protocols hitherto developed in quantum information. Changes in these entanglement properties of a tripartite state of electronic qubits on the inclusion of the spin-orbit interaction have also been discussed.