Contradictions between different measures of quantum uncertainty

Matía-Hernando, Paloma; Luis, Alfredo

doi:10.1103/physreva.86.052106

Cited by 6 publications

(14 citation statements)

References 92 publications

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“…The problem of quantifying quantum uncertainty can also be addressed with the standard deviation, the usual tool from statistical theory. These two measures are not necessarily consistent and there is a discussion about which one is the best to measure quantum uncertainty. There has been recent work on establishing uncertainty quantifiers , on generalizations of entropic uncertainty relations to include Renyi and Tsallis entropies and a discussion of inconsistencies between them and with the variance formulation .…”

Section: Introductionmentioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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Quantum uncertainties in position, momentum and phasespace are studied in the confined Harmonic Oscillator. Standard deviations and Shannon entropies are used to quantify these uncertainties and their behaviors are compared and contrasted. We observe a minimum in the momentum space Shannon entropy as the box length is increased, a feature that is not present in the momentum space standard deviation. The behaviors of the standard deviation product and the Shannon entropy sum, which form the basis of uncertainty relationships, are also analyzed. Maxima are observed in the product as the box length increases in sharp contrast to the entropy sum. The relationship between these behaviors and that of the Shannon entropy of the phase-space Wigner function is analyzed and discussed. An analysis of the energetic components is also performed. The results reinforce the idea that the confined Harmonic Oscillator can be considered as an intermediate model which interpolates between the Particle in a Box Model and the Harmonic Oscillator and thus contains characteristics of both models.

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Section: Introductionmentioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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“…Historically, the statistical inference about uncertainty is addressed by variance-based methods, mainly because they properly fit Gaussian statistics. Nevertheless, this may be not satisfactory enough in other situations, and alternative approaches may be of interest [4][5][6][7][8][9][10][11]. Previous works have already shown that different assessments of fluctuations may lead to contradictory and counterintuitive conclusions.…”

Section: Introductionmentioning

confidence: 99%

“…Previous works have already shown that different assessments of fluctuations may lead to contradictory and counterintuitive conclusions. For example, states with diverging variance may have arbitrary small entropy for the very same observable [9]. This ambiguity extends to the uncertainty relation between complementary observables when using Renyi-Tsallis entropic measures, since the very same state can be either of maximum or of minimum joint uncertainty, depending on the measure used [10].…”

Section: Introductionmentioning

confidence: 99%

Alternative measures of uncertainty in quantum metrology: Contradictions and limits

Luis

Rodil

2013

Phys. Rev. A

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We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of minute changes of physical quantities. We show that different measures lead to contradictory conclusions, including the possibility of arbitrarily small uncertainty for fixed resources. These intrinsic performances are compared with the averaged error in the corresponding estimation problem after single-shot measurements.

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“…The uncertainties can also be quantified by means of the Fisher information [42] and Tsallis and Rényi entropies [43], among others. The topic of which quantities are most consistent for to measure quantum uncertainty is object of discussion in the literature [44][45][46][47].…”

Section: Connection Between Information and Quantum Theoriesmentioning

confidence: 99%

Information and quantum theories: an analysis in one-dimensional systems

2020

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We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between information and quantum theories. In this context we determined the information entropies on position, S x , and momentum, S p , spaces, besides the entropy sum S t . Here, we use the modified entropic expressions that are dimensionally consistent. We provide original explanations for the behaviors of the S x , S p and S t values analyzing the probability densities and by means of the normalization constants and properties of Fourier transform. We validate the entropic uncertainty relation and inspect the standard deviation and information entropies as measures of quantum uncertainty. The systems of interest unidimensional one-particle quantum systems in ground and excited states.

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Contradictions between different measures of quantum uncertainty

Cited by 6 publications

References 92 publications

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Alternative measures of uncertainty in quantum metrology: Contradictions and limits

Information and quantum theories: an analysis in one-dimensional systems

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