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The full counting statistics of a non adiabatic pure spin pump are calculatedwith particular emphasis on the second and third moments. We show thatincoherence can change the sign of spin shot noise cross-correlations fromnegative to positive, implying entanglement for spin-singlet electronicsources, a truly counterintuitive result. The third moment on the other hand isshown to be much more resilient to incoherence.

Incoherence induced sign change in noise cross-correlations: A case study in the full counting statistics of a pure spin pump