Publisher’s Note: Stronger Uncertainty Relations for All Incompatible Observables [Phys. Rev. Lett.113, 260401 (2014)]

2015 ◽  
Vol 114 (3) ◽  
Author(s):  
Lorenzo Maccone ◽  
Arun K. Pati
Keyword(s):  
Uncertainty Relations ◽  
Incompatible Observables

scholarly journals Experimental investigation of the stronger uncertainty relations for all incompatible observables

2016 ◽  
Vol 93 (5) ◽  
Author(s):  
Kunkun Wang ◽  
Xiang Zhan ◽  
Zhihao Bian ◽  
Jian Li ◽  
Yongsheng Zhang ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Uncertainty Relations ◽  
Incompatible Observables

scholarly journals Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables

2017 ◽  
Vol 33 (1) ◽  
Author(s):  
Hung Quang Nguyen ◽  
Tu Quang Bui
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Schwarz Inequality ◽  
Uncertainty Relations ◽  
Heisenberg Uncertainty Relation ◽  
Generalized Uncertainty Relation ◽  
Heisenberg Uncertainty ◽  
Incompatible Observables

We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a generalization of the Cauchy-Schwarz inequality for two sets of vectors. Simple consequences of the N-ary uncertainty relation are also discussed. Keywords: Generalized uncertainty relation, Generalized uncertainty principle, Generalized Cauchy-Schwarz inequality.

scholarly journals Unified and Exact Framework for Variance-Based Uncertainty Relations

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiao Zheng ◽  
Shao-Qiang Ma ◽  
Guo-Feng Zhang ◽  
Heng Fan ◽  
Wu-Ming Liu
Keyword(s):  
Uncertainty Relation ◽  
Hermitian Operator ◽  
Uncertainty Relations ◽  
Unified Framework ◽  
Incompatible Observables

AbstractWe provide a unified and exact framework for the variance-based uncertainty relations. This unified framework not only recovers some well-known previous uncertainty relations, but also fixes the deficiencies of them. Utilizing the unified framework, we can construct the new uncertainty relations in both product and sum form for two and more incompatible observables with any tightness we require. Moreover, one can even construct uncertainty equalities to exactly express the uncertainty relation by the unified framework, and the framework is therefore exact in describing the uncertainty relation. Some applications have been provided to illustrate the importance of this unified and exact framework. Also, we show that the contradiction between uncertainty relation and non-Hermitian operator, i.e., most of uncertainty relations will be violated when applied to non-Hermitian operators, can be fixed by this unified and exact framework.

scholarly journals Entropic uncertainty relation under correlated dephasing channels

2018 ◽  
Vol 96 (7) ◽  
pp. 700-704 ◽  
Author(s):  
Göktuğ Karpat
Keyword(s):  
Quantum Mechanics ◽  
Standard Deviation ◽  
Lower Bound ◽  
Quantum System ◽  
Quantum Channel ◽  
Uncertainty Relation ◽  
Open Quantum System ◽  
Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Incompatible Observables

Uncertainty relations are a characteristic trait of quantum mechanics. Even though the traditional uncertainty relations are expressed in terms of the standard deviation of two observables, there exists another class of such relations based on entropic measures. Here we investigate the memory-assisted entropic uncertainty relation in an open quantum system scenario. We study the dynamics of the entropic uncertainty and its lower bound, related to two incompatible observables, when the system is affected by noise, which can be described by a correlated Pauli channel. In particular, we demonstrate how the entropic uncertainty for these two incompatible observables can be reduced as the correlations in the quantum channel grow stronger.

scholarly journals Variance-based uncertainty relations for incompatible observables

2016 ◽  
Vol 15 (9) ◽  
pp. 3909-3917 ◽  
Author(s):  
Bin Chen ◽  
Ning-Ping Cao ◽  
Shao-Ming Fei ◽  
Gui-Lu Long
Keyword(s):  
Uncertainty Relations ◽  
Incompatible Observables

The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
Uncertainty Principle ◽  
Large Scale ◽  
Uncertainty Relations ◽  
Speed Of Light ◽  
Energy Fluctuation ◽  
Hydrodynamic Analogy ◽  
Non Local ◽  
Minimum Uncertainty ◽  
Quantum Hydrodynamic ◽  
Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

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