FidelityAnchors

Fidelity against Fock-basis values the covariance formula never sees

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Test	What it does	Result
test_coherent_pair	Two coherent states overlap as $\exp (-|d{|}^2/2)$ under $\alpha =(x+ip)/\sqrt{2}$ -- the factor of 2 that the $\sqrt{2}$ in the quadratures hides.	✅ pass
test_coherent_thermal	$F(|\alpha ⟩,{\rho }_{th})=\exp (-|\alpha {|}^2/(\overline{n}+1))/(\overline{n}+1)$, $\pi$ times the thermal Husimi $Q$: the one anchor pinning both prefactor and exponent.	✅ pass
test_self_identity	$F(\rho ,\rho )=1$ for coherent, squeezed, thermal, displaced-squeezed and vacuum states.	✅ pass
test_thermal_pair	Two thermal states match the Fock-basis sum $1/((n_1+1)(n_2+1)(1-\sqrt{x_1{x}_2}{)}^2)$, exercising the $\mathrm{\Lambda }$ term that is zero for every pure pair.	✅ pass
test_vacuum_squeezed	$F(|0⟩,S(r)|0⟩)=1/\cosh r$.	✅ pass
test_vacuum_thermal	$F(|0⟩,{\rho }_{th})=1/(\overline{n}+1)$, the thermal ground-state weight.	✅ pass