Journal of Physics A Mathematical and General · 2002 · 29 citations · 9 references
Natural SciencesMathematicsPhysicsQuantum MechanicsDensity Matrix FormalismHilbert Space FormalismMetric GeometryMetric SpacesQuantum OperatorsQuantum StatesDensity MatricesDensity MatrixDensity OperatorsHilbert Space RepresentationsOperatorsQuantum Density MatrixQuantum State Representation
This paper treats the isometries of metric spaces of quantum states. We consider two metrics on the set all quantum states, namely the Bures metric and the one which comes from the trace-norm. We describe all the corresponding (nonlinear) isometries and also present similar results concerning the space of all (non-normalized) density operators.
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The “transition probability” in the state space of a ∗-algebra
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Armin Uhlmann · Reports on Mathematical Physics · 2000 · 32 citations · Full text