Abstract
The metric underlying the mixed state geometric phase in unitary and nonunitary evolution [Phys. Rev. Lett. {\bf 85}, 2845 (2000); Phys. Rev. Lett. {\bf 93}, 080405 (2004)] is delineated. An explicit form for the line element is derived and shown to be related to an averaged energy dispersion in the case of unitary evolution. The line element is measurable in interferometry involving nearby internal states. Explicit geodesics are found in the single qubit case. It is shown how the Bures line element can be obtained by extending our approach to arbitrary decompositions of density operators. The proposed metric is applied to a generic magnetic system in a thermal state.
Highlights
A quantum-mechanical metric underlies the notion of statistical distance that measures the distinguishability of quantum states [1,2]
The geometric phase (GP) can be taken as the Uhlmann holonomy [15] with the corresponding Bures metric [16] both arising from the horizontal lift to the possible decompositions of density operators
A key point of the mixed state GP is that it is operational in the sense that it is directly accessible in interferometry
Summary
A quantum-mechanical metric underlies the notion of statistical distance that measures the distinguishability of quantum states [1,2]. The GP can be taken as the Uhlmann holonomy [15] with the corresponding Bures metric [16] both arising from the horizontal lift to the possible decompositions of density operators. The mixed state geometric phase (GP) in unitary [17] and nonunitary [18] evolution has been proposed as an alternative to Uhlmann’s holonomy along paths of density operators. A key point of the mixed state GP is that it is operational in the sense that it is directly accessible in interferometry It has been studied on different experimental platforms [19,20,21]. We further discuss various applications of this metric as well as its relation to the Bures’ metric
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