Experimental test of tight state-independent preparation uncertainty relations for qubits

Sponar, Stephan; Danner, Armin; Obigane, Kazuma; Hack, Simon; Hasegawa, Yuji

doi:10.1103/physreva.102.042204

Cited by 11 publications

(5 citation statements)

References 42 publications

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“…However, this relation for projective measurements is outperformed by general, or more precisely positive-operator-valuedmeasures (POVM). This is demonstrated in a neutron polarimetric experiment for a four-outcome POVM in [161] and for a three-outcome POVM in [156], respectively (see [162] for a review of entropic uncertainty relations).…”

Section: Ii4 Uncertainty Relationsmentioning

confidence: 87%

Tests of Fundamental Quantum Mechanics and Dark Interactions with Low Energy Neutrons -- Extended Version

Sponar,

Sedmik,

Pitschmann

et al. 2020

Preprint

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Among the known particles, the neutron takes a special position, as it provides experimental access to all four fundamental forces and a wide range of hypothetical interactions. Despite being unstable, free neutrons live long enough to be used as test particles in interferometric, spectroscopic, and scattering experiments probing low-energy scales. As was already recognized in the 1970s, fundamental concepts of quantum mechanics can be tested in neutron interferometry using silicon perfect-single-crystals. Besides allowing for tests of uncertainty relations, Bell inequalities and alike, neutrons offer the opportunity to observe the effects of gravity and hypothetical dark forces acting on extended matter wave functions. Such tests gain importance in the light of recent discoveries of inconsistencies in our understanding of cosmology as well as the incompatibility between quantum mechanics and general relativity. Experiments with low-energy neutrons are thus indispensable tools for probing fundamental physics and represent a complementary approach to colliders. In this review we discuss the history and experimental methods used at this low-energy frontier of physics and collect bounds and limits on quantum mechanical relations and dark energy interactions.

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Section: Ii4 Uncertainty Relationsmentioning

confidence: 87%

Tests of Fundamental Quantum Mechanics and Dark Interactions with Low Energy Neutrons -- Extended Version

Sponar,

Sedmik,

Pitschmann

et al. 2020

Preprint

Self Cite

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show abstract

“…The uncertainty principle rules out the possibility to obtain precise measurement outcomes simultaneously when one measures two incomparable observables at the same time. Since the uncertainty relation satisfied by the position and momentum [1], various uncertainty relations have been extensively investigated [2][3][4][5][6][7]. On the occasion of celebrating the 125th anniversary of the academic journal "Science", the magazine listed 125 challenging scientific problems [8].…”

Section: Introductionmentioning

confidence: 99%

Probability density functions of quantum mechanical observable uncertainties

Zhang,

Huang,

Wang

et al. 2022

Preprint

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We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the supports of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state independent uncertainty relations. Our results may be generalized to multiple observable case in higher dimensional spaces.

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“…The uncertainty principle rules out the possibility to obtain precise measurement outcomes simultaneously when one measures two incomparable observables at the same time. Since the uncertainty relation is satisfied by the position and momentum [1], various uncertainty relations have been extensively investigated [2][3][4][5][6][7]. On the occasion of celebrating the 125th anniversary of the academic journal 'Science', the magazine listed 125 challenging scientific problems [8].…”

Section: Introductionmentioning

confidence: 99%