Transition Probability (Fidelity) and Its Relatives

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Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.

Journal: Foundations of Physics - FOUND PHYS , vol. 41, no. 3, pp. 288-298, 2011

DOI: 10.1007/s10701-009-9381-y

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On the Riemannian metric on the space of density matrices (Citations: 6)

Jochen Dittmann

Journal: Reports on Mathematical Physics - REP MATH PHYS , vol. 36, no. 2, pp. 309-315, 1995
Bures geometry of the three-level quantum systems (Citations: 8)

Paul B. Slater

Journal: Journal of Geometry and Physics - J GEOM PHYSICS , vol. 39, no. 3, pp. 207-216, 2001
Geometry of positive operators and uhlmann's approach to the geometric phase (Citations: 2)

Gustavo Corach, Alejandra L. Maestripieri

Journal: Reports on Mathematical Physics - REP MATH PHYS , vol. 47, no. 2, pp. 287-299, 2001
A certain class of Einstein-Yang-Mills systems (Citations: 5)

Gerd Rudolph, Torsten Tok

Journal: Reports on Mathematical Physics - REP MATH PHYS , vol. 39, no. 3, pp. 433-446, 1997
Parallel transport and “quantum holonomy” along density operators (Citations: 49)

A Uhlmann

Journal: Reports on Mathematical Physics - REP MATH PHYS , vol. 24, no. 2, pp. 229-240, 1986


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Keywords (5)

References (28)

On the Riemannian metric on the space of density matrices (Citations: 6)

Bures geometry of the three-level quantum systems (Citations: 8)

Geometry of positive operators and uhlmann's approach to the geometric phase (Citations: 2)

A certain class of Einstein-Yang-Mills systems (Citations: 5)

Parallel transport and “quantum holonomy” along density operators (Citations: 49)