Metrics

Timing for qudit's built-in quantum information metrics on random density matrices of increasing dimension $d\times d$.

No cross-framework comparison — benchmarks show internal scaling behaviour.

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Fidelity

Uhlmann fidelity $F(\rho ,\sigma )={\left(\mathrm{Tr}\sqrt{\sqrt{\rho }\sigma \sqrt{\rho }}\right)}^2$.

Von Neumann Entropy

$S(\rho )=-\mathrm{Tr}(\rho \log \rho )$.

Mutual Information

$I(A:B)=S({\rho }_A)+S({\rho }_B)-S({\rho }_{AB})$ on a $d^2\times d^2$ bipartite system.

Trace Distance

$D(\rho ,\sigma )=\frac{1}{2}\mathrm{Tr}|\rho -\sigma |$.

Bures Distance

$D_B(\rho ,\sigma )=\sqrt{2-2\sqrt{F(\rho ,\sigma )}}$.