A generalized Pancharatnam geometric phase formula for three-level quantum systems

Arvind, .; Mallesh, K. S.; Mukunda, N.

doi:10.1088/0305-4470/30/7/021

Cited by 96 publications

(120 citation statements)

References 13 publications

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“…We have introduced the factor √ 3 in such a way that for a pure state n · n = 1 [53], although other choices can be found in the literature. One first option would be to define [9] …”

Section: B Three-dimensional Fieldsmentioning

confidence: 99%

“…The structure constants f rst are elements of a completely antisymmetric tensor spelled out explicitly in Ref. [53], whose notation we follow. A particular feature of the generators of SU(3) in the defining 3 × 3 matrix representation is closure under anticommutation, { r , s } = 4 3 δ rs 1 1 + 2d rst t ,…”

Section: Appendix: Basic Facts and Parametrization Of Su(3)mentioning

confidence: 99%

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Classical distinguishability as an operational measure of polarization

et al. 2014

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We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.

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“…We have introduced the factor √ 3 in such a way that for a pure state n · n = 1 [53], although other choices can be found in the literature. One first option would be to define [9] …”

Section: B Three-dimensional Fieldsmentioning

confidence: 99%

Section: Appendix: Basic Facts and Parametrization Of Su(3)mentioning

confidence: 99%

Classical distinguishability as an operational measure of polarization

et al. 2014

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“…This generalized Bloch representation of density matrices for arbitrary N was introduced by Hioe and Eberly [9], and recently used in [10]. The case N = 3, related to the Gell-Mann matrices, is discussed in detail in the paper by Arvind et al [11]. The generalized Bloch vector τ (also called coherence vector) is D dimensional.…”

Section: Geometry Of Mn With Respect To the Hilbert-schmidt Metricmentioning

confidence: 99%

Hilbert–Schmidt volume of the set of mixed quantum states

Życzkowski

Sommers

2003

J. Phys. A: Math. Gen.

131

268

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We compute the volume of the convex N 2 − 1 dimensional set MN of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper-area of the boundary of this set is also found and its ratio to the volume provides an information about the complex structure of MN . Similar investigations are also performed for the smaller set of all real, symmetric density matrices.As an intermediate step we analyze volumes of the unitary and orthogonal groups and of the flag manifolds.

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“…2b. The angles (ϑ 1 , ϑ 2 ) describe a point in the positive octant of a sphere S 2 (or in an equilateral triangle, which is topologically equivalent) which represents the entire 2-torus formed from both phases ϕ i [45]. Each point on one the three edges of the octant represents a circle, so each entire edge corresponds to a sphere.…”

Section: B the 2 × 2 System-only One Ordering Of Pure Statesmentioning

confidence: 99%

Relativity of Pure States Entanglement

Życzkowski

Bengtsson

2002

Annals of Physics

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Entanglement of any pure state of an N × N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N ≥ 3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the "Future," the "Past," and the set of noncomparable states. C 2002 Elsevier Science (USA)

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A generalized Pancharatnam geometric phase formula for three-level quantum systems

Cited by 96 publications

References 13 publications

Classical distinguishability as an operational measure of polarization

Classical distinguishability as an operational measure of polarization

Hilbert–Schmidt volume of the set of mixed quantum states

Relativity of Pure States Entanglement

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