Trace-overlap gate fidelity ($\mathcal{F}=|\mathrm{tr}(U^{†}V)|/d$)

For two $d$-dimensional unitary matrices, this normalized absolute trace lies in $[0,1]$ and equals one exactly when $V=e^{i\gamma }U$. The triangle inequality on the eigenphases of $U^{†}V$ proves both statements. It ignores an overall global phase and compares complete propagators. It is not the same definition as average gate fidelity; for unitary implementations that latter quantity is $(d{\mathcal{F}}^2+1)/(d+1)$.