Two quasi-Hermitian observables are mutually compatible exactly when the matrix connecting their eigenvector frames can be scaled by positive diagonal matrices into a unitary matrix.
On the metric operator for the imagina ry cubic oscillator
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Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
Two quasi-Hermitian observables are mutually compatible exactly when the matrix connecting their eigenvector frames can be scaled by positive diagonal matrices into a unitary matrix.