A Stronger Multi-observable Uncertainty Relation

Song, Qiu-Cheng; Li, Junli; Peng, Guang-Xiong; Qiao, C. F.

doi:10.1038/srep44764

Cited by 44 publications

(32 citation statements)

References 29 publications

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“…Our results on the variance-based uncertainty relations of equations (16)(17) agrees with the predictions of quantum mechanics, and also with previous measurements using single photon sources, e.g. see Figures 2 and 3 in Ref.…”

Section: Experimental Implementationsupporting

confidence: 91%

Experimental investigation of the uncertainty relations with coherent light

Hui

Wang

et al. 2019

Quantum Inf Process

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Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system. Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system.

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Section: Experimental Implementationsupporting

confidence: 91%

Experimental investigation of the uncertainty relations with coherent light

Hui

Wang

et al. 2019

Quantum Inf Process

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“…With the qubit-system experiments, the results verify the validity of these uncertainty relations, and the superiority of our proposed uncertainty relations [17,33] is also exhibited.…”

Section: Introductionmentioning

confidence: 51%

“…which has a tighter lower bound than the relation (7) [32], but it is not always tighter than the inequality (8) [33].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…The generalization and improvement mainly focused on the uncertainty relation capable of dealing with more than two incompatible observables, i.e., the Heisenberg-type uncertainty relation for three canonical observables [27], uncertainty relations for angular momentum [28], and arbitrary incompatible observables [17]. There are also uncertainty relations with even more incompatible observables formulated in products [29,30] or sums [31][32][33] of variances.…”

Section: Introductionmentioning

confidence: 99%

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Experimental investigation of multi-observable uncertainty relations

Chen

Song

et al. 2017

Phys. Rev. A

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The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved lower bounds and were deemed capable of incorporating multiple observables. Here we report an experimental verification of seven uncertainty relations of this type with single-photon measurements. The results, while confirming these uncertainty relations, show as well the relative stringency of various uncertainty lower bounds.

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“…Namely, the Heisenberg-type uncertainty relation for three canonical observables is introduced in [50] and for arbitrary incompatible observables in [51]. The relations for more incompatible observables can be found in [52,53]. One can see, that in practice more then two incompatible observables can appear in the measurement, it is important to study uncertainty relations for many incompatible observables.…”

Section: Physical Applicationmentioning

confidence: 99%

Malevich’s Suprematist Composition Picture for Spin States

Man’ko

Markovich

2019

Entropy

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This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

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A Stronger Multi-observable Uncertainty Relation

Cited by 44 publications

References 29 publications

Experimental investigation of the uncertainty relations with coherent light

Experimental investigation of the uncertainty relations with coherent light

Experimental investigation of multi-observable uncertainty relations

Malevich’s Suprematist Composition Picture for Spin States

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