Experimental investigation of multi-observable uncertainty relations

Chen, Zhuo; Li, Junli; Song, Qiu-Cheng; Wang, Hui; Zangi, S. M.; Qiao, C. F.

doi:10.1103/physreva.96.062123

Cited by 26 publications

(25 citation statements)

References 36 publications

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“…is the triple constant given in the uncertain relations in [21,22]. From formulae (4), (8) and (12), we immediately get that in region 1, our Pauli B 2 -distances is in accordance with the uncertainty relation.…”

Section: The Pauli B -Distance Of Qubit Statementioning

confidence: 58%

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Liang¹,

Li²,

Ye³

et al. 2018

Quantum Inf Process

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We consider the optimal approximation of arbitrary qubit states with respect to an available states consisting the eigenstates of two of three Pauli matrices, the B 2 -distance of an arbitrary target state. Both the analytical formulae of the B 2 -distance and the corresponding complete optimal decompositions are obtained. The tradeoff relations for both the sum and the squared sum of the B 2 -distances have been analytically and numerically investigated.

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Section: The Pauli B -Distance Of Qubit Statementioning

confidence: 58%

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Liang¹,

Li²,

Ye³

et al. 2018

Quantum Inf Process

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“…The latter relations were experimentally verified in [54] using the single-photon measurement experiments. The inequalities (35), (34) and (39) have more stringent bounds than others in qubit systems.…”

Section: Measurements In Qubit Systemmentioning

confidence: 69%

“…In [54,55] an experimental investigation of several Heisenberg-type uncertainty relations is reported. In our turn, we rewrite Malevich's inequalities for the single qubit and qutrit in terms of the measurable observables to obtain inequalities similar to those, verified experimentally in the articles listed.…”

Section: Physical Applicationmentioning

confidence: 99%

“…Our Malevich's inequality for the single qubit, compared with eight uncertainty relations known from the literature, showed one of the best lower bounds according to MMC simulation. Further, Malevich's inequality for the qutrit system was rewritten in experimentally measurable observables, that allows its experimental verification along with several known inequalities provided in [53,54]. Thus, Malevich's inequalities can serve as uncertainty relations for the systems of high dimensions and successfully compete with already known inequalities.…”

Section: Physical Applicationmentioning

confidence: 99%

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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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“…This uncertainty relation was demonstrated for the N = 3 case by using single photons through SPDC [25].…”

Section: The Stokes Parametersmentioning

confidence: 70%

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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Experimental investigation of multi-observable uncertainty relations

Cited by 26 publications

References 36 publications

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Complete optimal convex approximations of qubit states under $$B_2$$ B 2 distance

Malevich’s Suprematist Composition Picture for Spin States

Experimental investigation of the uncertainty relations with coherent light

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