Wootters? distance revisited: a new distinguishability criterium

Majtey, Ana P.; Lamberti, Pedro W.; Martín, María Teresa; Plastino, A.

doi:10.1140/epjd/e2005-00005-1

Cited by 56 publications

(73 citation statements)

References 17 publications

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“…In this second case we need a metric in the space of distributions. The relation between these two distances in two different spaces has been studied for several choices of distances [8]. However the application of some of theses "distances" that do not satisfy the mathematical requirements of a "metric" (positivity, symmetry and triangular inequality) in an iterative algorithm is questionable.…”

Section: A Metric For Statesmentioning

confidence: 99%

State determination: An iterative algorithm

Goyeneche

Torre

2008

Phys. Rev. A

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Funes 3350, 7600 Mar del Plata, Argentina CONICET An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state Φ.Starting form an arbitrary state Ψ0, a succession of states Ψn is obtained that converges to Φ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.

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Section: A Metric For Statesmentioning

confidence: 99%

State determination: An iterative algorithm

Goyeneche

Torre

2008

Phys. Rev. A

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“…However, the distance K does not satisfy the triangle inequality and in addition is i) not symmetric ii) unbounded and iii) not always well defined [32]. To avoid these difficulties Rao and Lin [33,34] introduced a symmetrized version of K [32], the Jensen-Shannon divergence…”

Section: Measures Of Information Content and Information Dis-tancesmentioning

confidence: 99%

“…To avoid these difficulties Rao and Lin [33,34] introduced a symmetrized version of K [32], the Jensen-Shannon divergence…”

Section: Measures Of Information Content and Information Dis-tancesmentioning

confidence: 99%

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Information entropy, information distances, and complexity in atoms

Chatzisavvas

Moustakidis

Panos

2005

The Journal of Chemical Physics

165

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Shannon information entropies in position and momentum spaces and their sum are calculated as functions of Z (2 ≤ Z ≤ 54) in atoms. Roothaan-Hartree-Fock electron wave functions are used.The universal property S = a + b ln Z is verified. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescu's information energy and a complexity measure recently proposed. Shell effects at closed shells atoms are observed. The complexity measure shows local minima at the closed shells atoms indicating that for the above atoms complexity decreases with respect to neighboring atoms. It is seen that complexity fluctuates around an average value, indicating that the atom cannot grow in complexity as Z increases. Onicescu's information energy is correlated with the ionization potential. Kullback distance and Jensen-Shannon distance are employed to compare Roothaan-Hartree-Fock density distributions with other densities of previous works.

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“…It provides an embedding of the Fubini-Study metric [16,section IV], which gives the statistical distance between neighbouring pure quantum states (|ψ ) (cf [17]). Hübner gave an explicit formula for the Bures distance [18, p 240] (cf [19]),…”

Section: Bures Metricmentioning

confidence: 99%

Hilbert–Schmidt separability probabilities and noninformativity of priors

Slater

2006

J. Phys. A: Math. Gen.

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The Horodecki family employed the Jaynes maximum-entropy principle, fitting the mean (b 1 ) of the Bell-CHSH observable (B). This model was extended by Rajagopal by incorporating the dispersion σ 2 1 of the observable, and by Canosa and Rossignoli, by generalizing the observable (B α ). We further extend the Horodecki one-parameter model in both these manners, obtaining a three-parameter b 1 , σ 2 1 , α two-qubit model, for which we find a highly interesting/intricate continuum (−∞ < α < ∞) of Hilbert-Schmidt (HS) separability probabilities-in which, the golden ratio is featured. Our model can be contrasted with the three-parameter b q , σ 2 q , q one of Abe and Rajagopal, which employs a q(Tsallis)-parameter rather than α, and has simply q-invariant HS separability probabilities of 1 2. Our results emerge in a study initially focused on embedding certain information metrics over the two-level quantum systems into a q-framework. We find evidence, in this regard, that Srednicki's recently-stated biasedness criterion for noninformative priors yields rankings of priors fully consistent with an information-theoretic test of Clarke, previously applied to quantum systems by Slater.

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Wootters? distance revisited: a new distinguishability criterium

Cited by 56 publications

References 17 publications

State determination: An iterative algorithm

State determination: An iterative algorithm

Information entropy, information distances, and complexity in atoms

Hilbert–Schmidt separability probabilities and noninformativity of priors

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