2001
DOI: 10.1088/0305-4470/34/34/311
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The Monge metric on the sphere and geometry of quantum states

Abstract: Topological and geometrical properties of the set of mixed quantum states in the N −dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states and the generalised Husimi distributions to define the Monge distance between two arbitrary density matrices. The Monge metric has a simple semiclassical interpretation and induces a non-trivial geometry. Among all pure states the distance from the maximally mixed state ρ *… Show more

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Cited by 76 publications
(66 citation statements)
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“…In terms of Bloch vectors ̺ d , ̺, this induces the following S 2 distance between ̺ d and ̺, see e.g. [31]:…”
Section: Propositionmentioning
confidence: 99%
“…In terms of Bloch vectors ̺ d , ̺, this induces the following S 2 distance between ̺ d and ̺, see e.g. [31]:…”
Section: Propositionmentioning
confidence: 99%
“…Due to the trace-class constraint, the notion of distance between the densities ρ 1 and ρ 2 having the same purity is d(ρ 1 , ρ 2 ) = tr ρ 2 1 − tr (ρ 1 ρ 2 ), see e.g. [39], or in terms of ̺:…”
Section: A Gell-mann Basis and Adjoint Representationmentioning
confidence: 99%
“…Beyond the full pure and mixed state manifolds there are numerous other submanifolds that are of interest in physics; the volumes of which have already been calculated (see, for example, [3,11,21,31,32,33] and references within). These sub-manifolds and their volumes give us both a way to confirm our methodology, as well as offering a systematic, rather than numeric, way of computing such quantities.…”
Section: Other Su(n) and U(n) Coset Volumesmentioning
confidence: 99%