Sub-Poissonian and anti-bunching criteria via majorization of statistics

Medranda, Daniel G; Luis, Alfredo

doi:10.1088/1751-8113/48/25/255302

Cited by 3 publications

(1 citation statement)

References 38 publications

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“…In particular, majorization arises naturally in several problems of quantum information theory. A nonexhaustive list includes entanglement criteria [2,3], characterizing mixing and quantum measurements [4][5][6], majorization uncertainty relations [7][8][9][10][11][12] and quantum entropies [13][14][15][16], among others [17][18][19][20][21][22][23] (see also [24,25] for reviews of some of these topics).…”

Section: Introductionmentioning

confidence: 99%

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

Bosyk

Sergioli

Freytes

et al. 2017

Physica A: Statistical Mechanics and its Applications

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We study the problem of deterministic transformations of an initial pure entangled quantum state, |ψ , into a target pure entangled quantum state, |φ , by using local operations and classical communication (LOCC). A celebrated result of Nielsen [Phys. Rev. Lett. 83, 436 (1999)] gives the necessary and sufficient condition that makes this entanglement transformation process possible. Indeed, this process can be achieved if and only if the majorization relation ψ ≺ φ holds, where ψ and φ are probability vectors obtained by taking the squares of the Schmidt coefficients of the initial and target states, respectively. In general, this condition is not fulfilled. However, one can look for an approximate entanglement transformation. Vidal et. al [Phys. Rev. A 62, 012304 (2000)] have proposed a deterministic transformation using LOCC in order to obtain a target state |χ opt most approximate to |φ in terms of maximal fidelity between them. Here, we show a strategy to deal with approximate entanglement transformations based on the properties of the majorization lattice. More precisely, we propose as approximate target state one whose Schmidt coefficients are given by the supremum between ψ and φ. Our proposal is inspired on the observation that fidelity does not respect the majorization relation in general. Remarkably enough, we find that for some particular interesting cases, like two-qubit pure states or the entanglement concentration protocol, both proposals are coincident.

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Section: Introductionmentioning

confidence: 99%

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

Bosyk

Sergioli

Freytes

et al. 2017

Physica A: Statistical Mechanics and its Applications

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Sufficient conditions for the majorization ordering and their applications in some quantum information comparisons

Izadkhah

Amini-Seresht

Moradian

2023

Physica A: Statistical Mechanics and its Applications

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Majorization of quantum polarization distributions

Luis

Donoso

2016

Phys. Rev. A

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Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply majorization as a meta-measure of quantum polarization fluctuations, this is to say of the degree of polarization. We compare the polarization fluctuations of the most relevant classes of quantum and classical-like states. In particular we test Lieb's conjecture regarding classical-like states as the most polarized and a complementary conjecture that the most unpolarized pure states are the most nonclassical.

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Sub-Poissonian and anti-bunching criteria via majorization of statistics

Cited by 3 publications

References 38 publications

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

Sufficient conditions for the majorization ordering and their applications in some quantum information comparisons

Majorization of quantum polarization distributions

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