Entropic measures of joint uncertainty: Effects of lack of majorization

Luis, Alfredo; Bosyk, Gustavo Martín; Portesi, Mariela

doi:10.1016/j.physa.2015.10.097

Cited by 15 publications

(10 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previous works have found that different entropies lead to contradictory conclusions, where the minimum uncertainty states with one measure are the maximum uncertainty states of the other [22]. Majorization clearly explains this result showing that these contradictions arise because we are dealing with incomparable states [23].…”

Section: Discussionmentioning

confidence: 52%

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

Medranda¹,

Luis

2015

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Abstract. We use majorization and confidence intervals as a convenient tool to compare the uncertainty in photon number for different quantum light states. To this end majorization is formulated in terms of confidence intervals. As a suitable case study we apply this tool to sub-and super-Posissonian behavior and bunching and antibunching effects. We focus on the most significant classical and nonclassical states, such as Glauber coherent, thermal, photon number, and squeezed states. We show that majorization provides a more complete analysis that in some relevant situations contradicts the predictions of variance.

show abstract

Section: Discussionmentioning

confidence: 52%

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

Medranda¹,

Luis

2015

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…[11] is a quite interesting formulation particularly suited to phase-angle variables. We also show that this encounters fundamental ambiguities when contrasting different slightly different alternative implementations, as it also holds for other approaches [12][13][14].…”

Section: Introductionmentioning

confidence: 56%

“…We have successfully derived meaningful phase-number uncertainty relations from the Weyl form of commutation relations. This can be applied to study phasenumber statistical properties of meaningful field states, especially intermediate states that have already demonstrated interesting properties regarding uncertainty relations [7,13,14].…”

Section: Example: Phase-number Intermediate Statesmentioning

confidence: 99%

Phase–number uncertainty from Weyl commutation relations

Luis

Donoso

2017

Annals of Physics

Self Cite

View full text Add to dashboard Cite

We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spinlike systems, which is the case when describing the phase difference between two field modes, as well as to the phase and number of a single-mode field. Some contradictions between the product and sums of characteristic functions are noted.

show abstract

“…Lack of majorization relation between two beams just tell us that one must resort to particular criteria, selected according to the particular application, to evaluate whether a beam can be considered of better quality than a second beam or vice versa. The effects of lack of majorization have been studied in other contexts in [23]. A related question is whether exists a beam that majorizes any other beam, that is, an optimal quality beam.…”

Section: Intersecting Lorenz Curves and Contradicting Entropic Bementioning

confidence: 99%

Lorenz curve of a light beam: evaluating beam quality from a majorization perspective

2017

View full text Add to dashboard Cite

We introduce a novel approach for the characterization of the quality of a laser beam that is not based on particular criteria for beam width definition. The Lorenz curve of a light beam is a sophisticated version of the so-called power-in-the-bucket curve, formed by the partial sums of discretized joint intensity distribution in the near and far fields, sorted in decreasing order. According to majorization theory, a higher Lorenz curve implies that all measures of spreading in phase space, and, in particular, all Rényi (and Shannon) entropy-based measures of the beam width products in near and far fields, are unanimously smaller, providing a strong assessment of a better beam quality. Two beams whose Lorenz curves intersect can be considered of relatively better or lower quality only according to specific criteria, which can be inferred from the plot of the respective Lorenz curves.

show abstract

Entropic measures of joint uncertainty: Effects of lack of majorization

Cited by 15 publications

References 73 publications

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

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

Phase–number uncertainty from Weyl commutation relations

Lorenz curve of a light beam: evaluating beam quality from a majorization perspective

Contact Info

Product

Resources

About