Abstract
We study trace formulas for the exponentials of general fermion bilinears, including pairing terms and including non-Hermitian forms. In particular, we give elementary derivations for determinant and Pfaffian formulae for such traces and use these to obtain general expressions for the full counting statistics in states associated with quadratic Hamiltonians, including BCS-like pairing terms and fermion parity in a prescribed region or set of modes. We also derive Pfaffian expressions for state overlaps and counting statistics in states built out of the vacuum by creation of pairs of particles.
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