For zero-mean Gaussian states in free field theory, excitability from one state to another is equivalent to three explicit two-point-function conditions, and one-way excitability automatically implies two-way excitability (quasiequivalence).
Longo,Modular Structure of the Weyl Algebra,Commun
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Excitability in quantum field theory
For zero-mean Gaussian states in free field theory, excitability from one state to another is equivalent to three explicit two-point-function conditions, and one-way excitability automatically implies two-way excitability (quasiequivalence).