Geometric phases and related structures
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Publication:1372498
DOI10.1016/0034-4877(96)83640-8zbMath0891.46051OpenAlexW2101926530MaRDI QIDQ1372498
Publication date: 20 July 1998
Published in: Reports on Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0034-4877(96)83640-8
Berry phasedensity operatorstwo-level systemsmetric of Buresparallel transport of amplitudes and phasesReimann formstochastic mappings
General and philosophical questions in quantum theory (81P05) Applications of functional analysis in quantum physics (46N50)
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Cites Work
- A study on the geometry of pairs of positive linear forms, algebraic transition probability and geometrical phase over non-commutative operator algebras. II
- A gauge field governing parallel transport along mixed states
- A note on the transition probability over \(C^*\)-algebras
- Stochastic linear maps and transition probability
- On quantum holonomy for mixed states
- A remark on transition probability
- Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form
- Parallel transport and ``quantum holonomy along density operators
- On Cantoni's generalized transition probability
- One-parameter family of Radon-Nikodym theorems for states of a von Neumann algebra
- Functional calculus for sesquilinear forms and the purification map
- The transition probability in the state space of a \(^*\)-algebra
- Means of positive linear operators
- Density operators as an arena for differential geometry
- On a connection governing parallel transport along \(2 \times{}2\) density matrices
- Monotone metrics on matrix spaces
- Bures distance function and a generalization o f Sakai's non-commutative Radon-Nikodym theorem
- On equivalence of infinite product measures
- On the Bures Distance and the Uhlmann Transition Probability of States on a von Neumann Algebra
- Quantum statistical holonomy
- Quantal phase factors accompanying adiabatic changes
- The Transition Probability for States of *‐Algebras
- An Extended Cencov Characterization of the Information Metric
- Bures distance and relative entropy
- Statistical distance and the geometry of quantum states
- A class of connections governing parallel transport along density matrices
- Geometries of quantum states
- A Radon-Nikodym theorem in 𝑊*-algebras
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