Tomographic Entropy and New Entropic Uncertainty Relations

2007 ◽  
Author(s):  
Margarita A. Man'ko ◽  
Guillaume Adenier ◽  
Andrei Yu. Khrennikov ◽  
Pekka Lahti ◽  
Vladimir I. Man'ko ◽  
...  
Keyword(s):  
Uncertainty Relations ◽  
Entropic Uncertainty Relations ◽  
Tomographic Entropy

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

Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

2018 ◽  
Vol 17 (12) ◽  
Author(s):  
Dong Wang ◽  
Wei-Nan Shi ◽  
Ross D. Hoehn ◽  
Fei Ming ◽  
Wen-Yang Sun ◽  
...  
Keyword(s):  
Uncertainty Relations ◽  
Entropic Uncertainty Relations ◽  
Atom System

scholarly journals Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 763 ◽  
Author(s):  
Ana Costa ◽  
Roope Uola ◽  
Otfried Gühne
Keyword(s):  
Relative Entropy ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
W States ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Local Measurements ◽  
Action At A Distance ◽  
Quantum Steering ◽  
Joint Convexity

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

scholarly journals Entropic uncertainty relation in neutrino oscillations

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Dong Wang ◽  
Fei Ming ◽  
Xue-Ke Song ◽  
Liu Ye ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Correlation ◽  
Neutrino Oscillations ◽  
Quantum Information Processing ◽  
Physical Phenomenon ◽  
Uncertainty Relations ◽  
Classical Counterpart ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Neutrino Flavor ◽  
Potential Applications

Abstract Neutrino oscillation is deemed as an interesting physical phenomenon and shows the nonclassical features made apparently by the Leggett–Garg inequality. The uncertainty principle is one of the fundamental features that distinguishes the quantum world to its classical counterpart. And the principle can be depicted in terms of entropy, which forms the so-called entropic uncertainty relations (EUR). In this work, the entropic uncertainty relations that are relevant to the neutrino-flavor states are investigated by comparing the experimental observation of neutrino oscillations to predictions. From two different neutrino sources, we analyze ensembles of reactor and accelerator neutrinos for different energies, including measurements performed by the Daya Bay collaboration using detectors at 0.5 and 1.6 km from their source, and by the MINOS collaboration using a detector with a 735km distance to the neutrino source. It is found that the entropy-based uncertainty conditions strengths exhibits non-monotonic evolutions as the energy increases. We also quantify the systemic quantumness measured by quantum correlation, and derive the intrinsic relationship between quantum correlation and EUR. Furthermore, we utilize EUR as a criterion to detect entanglement of neutrino-flavor state. Our results could illustrate the potential applications of neutrino oscillations on quantum information processing in the weak-interaction processes.

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