Uncertainty relations expressed by Shannon-like entropies

Open Physics ◽  
2003 ◽  
Vol 1 (3) ◽  
Author(s):  
V. Majerník ◽  
Eva Majerníková ◽  
S. Shpyrko
Keyword(s):  
Shannon Entropy ◽  
Uncertainty Principle ◽  
Quantum Physics ◽  
Graphical Representations ◽  
Uncertainty Relations ◽  
Entropic Uncertainty Relations

AbstractBesides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

scholarly journals Entropic Uncertainty Relations, Entanglement and Quantum Gravity Effects via the Generalised Uncertainty Principle

2018 ◽  
pp. 1-12
Author(s):  
Otto Gadea ◽  
Gardo Blado
Keyword(s):  
Shannon Entropy ◽  
Uncertainty Principle ◽  
Upper Bound ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Single System ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Gravity Effects ◽  
Entanglement Criterion

We apply the generalised uncertainty principle (GUP) to the entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. We combine previous work on the Shannon entropy entanglement criterion for bipartite systems and the GUP corrections to the Shannon entropy for a single system to calculate the GUP correction for an entangled bipartite system. As in an earlier paper of the second author, which dealt with variance relations, it is shown that there is an increase in the upper bound for the entanglement condition upon the application of the generalised uncertainty principle. Necessary fundamental concepts of the generalised uncertainty principle, entanglement and the entropic uncertainty relations are also discussed. This paper puts together the concepts of entanglement, entropic uncertainty relations and the generalised uncertainty principle all of which have been separately discussed in pedagogical papers by Schroeder, Majernik et al., Blado et al. and Sprenger.  

Shannon information entropy for a one-dimensional ionic crystal

2019 ◽  
Vol 35 (07) ◽  
pp. 2050032
Author(s):  
Gabriel González ◽  
Daniel Salgado-Blanco
Keyword(s):  
Lattice Constant ◽  
Shannon Entropy ◽  
Ionic Crystal ◽  
Uncertainty Relations ◽  
Information Theoretic ◽  
One Dimensional ◽  
Dirac Delta ◽  
Entropic Uncertainty Relations ◽  
Shannon Information Entropy ◽  
The Stability

In this work, we present the information theoretic lengths given by Shannon and Fisher for the lowest-lying stationary state of a one-dimensional ionic crystal modeled by [Formula: see text] equally spaced attractive and repulsive Dirac delta potentials. The entropic uncertainty relations related to position and momentum spaces are studied as a function of the number of ions and the distance between them. Our results show that the stability of the ionic crystal depends on the number of ions and distance between them. In particular, we show that the position Shannon entropy is always positive and increases as the lattice constant between ions grows, in contrast with the momentum Shannon entropy which decreases and becomes negative beyond a particular lattice constant value.

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.

Ancient Philosophy, Quantum Reality and Management

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Anindo Bhattacharjee
Keyword(s):  
Uncertainty Principle ◽  
Quantum Physics ◽  
Ancient Philosophy ◽  
Physical World ◽  
Scientific Management ◽  
Werner Heisenberg ◽  
Deterministic Models ◽  
Late 19Th Century ◽  
Quantum Reality ◽  
New View

The romanticism of management for numbers, metrics and deterministic models driven by mathematics, is not new. It still exists. This is exactly the problem which classical physicists had in the late 19th century until Werner Heisenberg brought the uncertainty principle and opened the doors of quantum physics that challenged the deterministic view of the physical world mostly driven by the Newtonian view. In this paper, we propose an uncertainty principle of management and then list a set of factors which capture this uncertainty quite well and arrive at a new view of scientific management thought. The new view which we call as the Quantum view of Management (QVM) will be based on the major tenets from the ancient philosophical traditions viz., Jainism, Taoism, Advaita Vedanta, Buddhism, Greek philosophers (like Hereclitus) etc.

scholarly journals Tight entropic uncertainty relations for systems with dimension three to five

2017 ◽  
Vol 95 (3) ◽  
Author(s):  
Alberto Riccardi ◽  
Chiara Macchiavello ◽  
Lorenzo Maccone
Keyword(s):  
Uncertainty Relations ◽  
Entropic Uncertainty Relations

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

scholarly journals Entropic uncertainty relations under the relativistic motion

2013 ◽  
Vol 726 (1-3) ◽  
pp. 527-532 ◽  
Author(s):  
Jun Feng ◽  
Yao-Zhong Zhang ◽  
Mark D. Gould ◽  
Heng Fan
Keyword(s):  
Uncertainty Relations ◽  
Relativistic Motion ◽  
Entropic Uncertainty Relations

scholarly journals Entropic uncertainty relations

1984 ◽  
Vol 103 (5) ◽  
pp. 253-254 ◽  
Author(s):  
Iwo Bialynicki-Birula
Keyword(s):  
Uncertainty Relations ◽  
Entropic Uncertainty Relations
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