scholarly journals Measurements of Entropic Uncertainty Relations in Neutron Optics

2020 ◽  
Vol 10 (3) ◽  
pp. 1087 ◽  
Author(s):  
Bülent Demirel ◽  
Stephan Sponar ◽  
Yuji Hasegawa
Keyword(s):  
Neutron Spin ◽  
Uncertainty Relations ◽  
Joint Measurement ◽  
Neutron Optics ◽  
First Case ◽  
90Th Anniversary ◽  
Second Category ◽  
Error Correction Procedures ◽  
Projective Measurements ◽  
Positive Operator Valued Measure

The emergence of the uncertainty principle has celebrated its 90th anniversary recently. For this occasion, the latest experimental results of uncertainty relations quantified in terms of Shannon entropies are presented, concentrating only on outcomes in neutron optics. The focus is on the type of measurement uncertainties that describe the inability to obtain the respective individual results from joint measurement statistics. For this purpose, the neutron spin of two non-commuting directions is analyzed. Two sub-categories of measurement uncertainty relations are considered: noise–noise and noise–disturbance uncertainty relations. In the first case, it will be shown that the lowest boundary can be obtained and the uncertainty relations be saturated by implementing a simple positive operator-valued measure (POVM). For the second category, an analysis for projective measurements is made and error correction procedures are presented.

scholarly journals Approximate joint measurements of qubit observables

2008 ◽  
Vol 8 (8&9) ◽  
pp. 797-818
Author(s):  
P. Busch ◽  
T. Heinosaari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Uncertainty Relations ◽  
Joint Measurement ◽  
Joint Measurability ◽  
Heisenberg Type

Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of observables that can be characterized by a form of covariance. Here we investigate conditions for the joint measurability of arbitrary pairs of qubit observables. For pairs of noncommuting sharp qubit observables, a notion of approximate joint measurement is introduced. Optimal approximate joint measurements are shown to lie in the class of covariant joint measurements. The marginal observables found to be optimal approximators are generally not among the coarse-grainings of the observables to be approximated. This yields scope for the improvement of existing joint measurement schemes. Both the quality of the approximations and the intrinsic unsharpness of the approximators are shown to be subject to Heisenberg-type uncertainty relations.

scholarly journals Error-disturbance uncertainty relations studied in neutron optics

2016 ◽  
Vol 746 ◽  
pp. 012048
Author(s):  
Stephan Sponar ◽  
Georg Sulyok ◽  
Bulent Demirel ◽  
Yuji Hasegawa
Keyword(s):  
Uncertainty Relations ◽  
Neutron Optics

Error-disturbance uncertainty relations in neutron spin measurements

2016 ◽  
Vol 14 (04) ◽  
pp. 1640016
Author(s):  
Stephan Sponar
Keyword(s):  
Uncertainty Principle ◽  
Neutron Spin ◽  
Reciprocal Relation ◽  
Spin Component ◽  
Uncertainty Relations ◽  
Position Measurement ◽  
Wide Range ◽  
Heisenberg Type ◽  
Spin Measurements ◽  
Heisenberg's Uncertainty Principle

Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.

scholarly journals 3D printed magnets for neutron spin manipulation

2019 ◽  
Vol 219 ◽  
pp. 10008 ◽  
Author(s):  
Richard Wagner ◽  
Laurids Brandl ◽  
Wenzel Kersten ◽  
Stephan Sponar ◽  
Yuji Hasegawa ◽  
...  
Keyword(s):  
Spin Rotation ◽  
Wave Functions ◽  
Neutron Spin ◽  
Neutron Interferometry ◽  
Neutron Optics ◽  
Complex Shapes ◽  
New Type ◽  
3D Printed ◽  
Spin Flipper ◽  
Spinor Symmetry

Devices for manipulation of the neutron spin are vital for experiments in neutron optics such as neutron interferometry. Here we introduce a new type of such devices which are based on a magnetic material that can be 3D printed in complex shapes. We have constructed a spin flipper wherein the angle of spin rotation can be adjusted by variation of the distance between magnetized pieces. As the device does not contain any heat dissipating coils we expect interferometric measurements to become more stable and hence more accurate. Results of an experiment using polarized neutrons verify the device's functionality, and indicate the potential of the new method. A second experiment for demonstration of the 4π spinor symmetry of fermionic wave functions is in progress.

scholarly journals Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 270 ◽  
Author(s):  
Kyunghyun Baek ◽  
Hyunchul Nha ◽  
Wonmin Son
Keyword(s):  
Three Dimensional ◽  
Uncertainty Relations ◽  
Dimensional System ◽  
Direct Sum ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
Uncertainty Bound ◽  
Three Dimensional System ◽  
Unsharp Observables ◽  
Positive Operator Valued Measure

We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches (Friendland, S.; Gheorghiu, V.; Gour, G. Phys. Rev. Lett. 2013, 111, 230401; Rastegin, A.E.; Życzkowski, K. J. Phys. A, 2016, 49, 355301), particularly by extending the direct-sum majorization relation first introduced in (Rudnicki, Ł.; Puchała, Z.; Życzkowski, K. Phys. Rev. A 2014, 89, 052115). We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen–Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

PROBABILISTIC REMOTELY PREPARING AN ARBITRARY TWO-PARTICLE ENTANGLED STATE VIA POSITIVE OPERATOR-VALUED MEASURE

2008 ◽  
Vol 06 (06) ◽  
pp. 1183-1193 ◽  
Author(s):  
KUI HOU ◽  
JING WANG ◽  
SHOU-HUA SHI
Keyword(s):  
Positive Operator ◽  
Cluster State ◽  
Success Probability ◽  
Remote State Preparation ◽  
Entangled State ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
State Preparation ◽  
Projective Measurements ◽  
Positive Operator Valued Measure

By means of the method of the positive operator-valued measure, two schemes to remotely prepare an arbitrary two-particle entangled state were presented. The first scheme uses a one-dimensional four-particle non-maximally entangled cluster state while the second one uses two partially entangled two-particle states as the quantum channel. For both schemes, if Alice performs two-particle projective measurements and Bob adopts positive operator-valued measure, the remote state preparation can be successfully realized with certain probability. The success probability of the remote state preparation and classical communication cost are calculated. It is shown that Bob can obtain the unknown state with probability 1/4 for maximally entangled state. However, for four kinds of special states, the success probability of preparation can be enhanced to unity.

Neutron optics and neutron forward-scattering using a transverse neutron-spin-echo instrument

1995 ◽  
Vol 213-214 ◽  
pp. 842-844 ◽  
Author(s):  
Masahiro Hino ◽  
Norio Achiwa ◽  
Seiji Tasaki ◽  
Toru Ebisawa ◽  
Tsunekazu Akiyoshi
Keyword(s):  
Spin Echo ◽  
Forward Scattering ◽  
Neutron Spin ◽  
Neutron Spin Echo ◽  
Neutron Optics

scholarly journals Error-Disturbance Uncertainty Relations in Neutron-Spin Measurements

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Stephan Sponar ◽  
Georg Sulyok ◽  
Jaqueline Erhart ◽  
Yuji Hasegawa
Keyword(s):  
Neutron Spin ◽  
Spin Component ◽  
Uncertainty Relations ◽  
Seminal Paper ◽  
Test Error ◽  
Optical Experiment ◽  
Wide Range ◽  
Experimental Parameters ◽  
Spin Measurements

In his seminal paper, which was published in 1927, Heisenberg originally introduced a relation between the precision of a measurement and the disturbance it induces onto another measurement. Here, we report a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on a measurement of another spin-component to test error-disturbance uncertainty relations (EDRs). We demonstrate that Heisenberg’s original EDR is violated and the Ozawa and Branciard EDRs are valid in a wide range of experimental parameters.

scholarly journals Additivity of entropic uncertainty relations

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 59 ◽  
Author(s):  
René Schwonnek
Keyword(s):  
Uncertainty Relation ◽  
Natural Generalization ◽  
Uncertainty Relations ◽  
Entanglement Witness ◽  
Separable States ◽  
Entropic Uncertainty Relations ◽  
Multipartite System ◽  
Positive Coefficients ◽  
Global Uncertainty ◽  
Projective Measurements

We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.

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