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Fix typo in Bures comparison #421

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Sep 5, 2024
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Fix typo in Bures comparison #421

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9 changes: 6 additions & 3 deletions docs/source/comparing.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -115,14 +115,17 @@ The normalized Bures similarity (NBS) is defined as:
.. math::

NBS(K_1, K_2) = \frac{\mathcal{F}(K_1, K_2)}{\sqrt{\operatorname{Tr}[K_1] \operatorname{Tr}[K_2]}}
\mathcal{F}(K_1, K_2) = \operatorname{Tr}[(K_1^{1/2}K_2K_1^{1/2})^{1/2}]

and :math:`\mathcal{F}` is known as the fidelity.
where :math:`\mathcal{F}` is known as the fidelity.

.. math::

\mathcal{F}(K_1, K_2) = \operatorname{Tr}[(K_1^{1/2}K_2K_1^{1/2})^{1/2}]

and relatedly the Bures distance :math:`\mathcal{B}`, a proper metric is defined as:

.. math::
\mathcal{B}^2(K_1, K_2) = \operatorname{Tr}[K_1] \operatorname{Tr}[K_2] - 2 \operatorname{Tr}[(K_1^{1/2}K_2K_1^{1/2})^{1/2}]
\mathcal{B}^2(K_1, K_2) = \operatorname{Tr}[K_1] + \operatorname{Tr}[K_2] - 2 \operatorname{Tr}[(K_1^{1/2}K_2K_1^{1/2})^{1/2}]



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