FidelityAlgebra

Symmetry, range, unitary invariance and agreement with the overlap

5/5 passed in 117ms

Test	What it does	Result
test_pure_overlap	$F=\mathrm{Tr}(\rho \sigma )$ with a pure state on one side, where $\mathrm{\Lambda }$ vanishes.	✅ pass
test_range	$0\le F\le 1$ over 60 random mixed pairs, with no clamping to make it true.	✅ pass
test_symmetry	$F(a,b)=F(b,a)$ over 40 random mixed single-mode pairs.	✅ pass
test_two_mode_pure	Two pure two-mode squeezed vacua take the n-mode pure branch and match the Fock-basis overlap $1/({\cosh }^2{r}_1{\cosh }^2{r}_2(1-t_1{t}_2{)}^2)$ with $t=\tanh r$.	✅ pass
test_unitary_invariance	A common symplectic unitary leaves $F$ unchanged: $F(Ua{U}^{†},Ub{U}^{†})=F(a,b)$.	✅ pass