Bures Metric - Bures Distance

Bures Distance

The Bures distance is the finite version of the infinitesimal square distance described above and is given by

D_B(\rho_1,\rho_2)^2 = 2(1-\sqrt{F(\rho_1,\rho_2)}),

where the fidelity function is defined as

F(\rho_1,\rho_2) = \left^2

Another associated function is the Bures arc also known as Bures angle, Bures length or quantum angle, defined as

D_A(\rho_1,\rho_2) = \arccos \sqrt{F(\rho_1,\rho_2)},

which is a measure of the statistical distance between the quantum states.

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