scholarly journals Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations

2021 ◽  
Vol 7 (1) ◽  
pp. eabd2986
Author(s):  
Zhibo Hou ◽  
Jun-Feng Tang ◽  
Hongzhen Chen ◽  
Haidong Yuan ◽  
Gou-Yong Xiang ◽  
...  
Keyword(s):  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Quantum Metrology ◽  
Trade Off ◽  
Practical Applications ◽  
Multiple Parameters ◽  
Classical Scheme ◽  
Precision Limit ◽  
Heisenberg Uncertainty ◽  
Heisenberg Uncertainty Relations

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

scholarly journals Heisenberg uncertainty relations for photons

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
Iwo Bialynicki-Birula ◽  
Zofia Bialynicka-Birula
Keyword(s):  
Uncertainty Relations ◽  
Heisenberg Uncertainty ◽  
Heisenberg Uncertainty Relations

Quantization of the momentum of an electromagnetic field in atoms and selection rules for optical transitions

2021 ◽  
pp. 2150267
Author(s):  
S. A. Pyroha
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Minimum Energy ◽  
Uncertainty Relations ◽  
Stationary States ◽  
Physical Reason ◽  
Selection Rules ◽  
Transition Mechanism ◽  
Heisenberg Uncertainty ◽  
Heisenberg Uncertainty Relations

The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is [Formula: see text]. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Lijun Song ◽  
Xiaoguang Wang ◽  
Dong Yan ◽  
Yongda Li
Keyword(s):  
Uncertainty Relation ◽  
Sufficient Conditions ◽  
Entangled States ◽  
Uncertainty Relations ◽  
Heisenberg Uncertainty Relation ◽  
Partial Transposition ◽  
Heisenberg Uncertainty ◽  
Entanglement Conditions

AbstractFrom the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.

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