scholarly journals A holographic proof of Rényi entropic inequalities

2016 ◽  
Vol 2016 (12) ◽  
Author(s):  
Yuki Nakaguchi ◽  
Tatsuma Nishioka
Keyword(s):  
Entropic Inequalities

Theoretical and Experimental Characterization of Entropic Inequalities

2007 ◽  
Author(s):  
Fabio Antonio Bovino ◽  
Concita Sibilia ◽  
Diederik S. Wiersma
Keyword(s):  
Experimental Characterization ◽  
Entropic Inequalities

Criteria for equality in two entropic inequalities

2014 ◽  
Vol 205 (7) ◽  
pp. 1045-1068 ◽  
Author(s):  
M E Shirokov
Keyword(s):  
Entropic Inequalities

scholarly journals Tests for quantum contextuality in terms of Q-entropies

2014 ◽  
Vol 14 (11&12) ◽  
pp. 996-1013
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Theoretic Approach ◽  
Entropic Inequalities ◽  
Information Theoretic ◽  
The Family ◽  
Information Theoretic Approach ◽  
New Inequalities

The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser--Horne--Shimony--Holt (CHSH) and Klyachko--Can--Binicio\v{g}lu--Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.

scholarly journals Direct Measurement of Nonlinear Properties of Bipartite Quantum States

2006 ◽  
Vol 13 (03) ◽  
pp. 281-289
Author(s):  
F. A. Bovino ◽  
G. Castagnoli ◽  
A. Ekert ◽  
C. Moura Alves ◽  
P. Horodecki ◽  
...  
Keyword(s):  
Information Science ◽  
Quantum States ◽  
Full Description ◽  
Entangled Photons ◽  
Entanglement Witness ◽  
Entropic Inequalities ◽  
Nonlinear Properties ◽  
Local Measurements ◽  
Marking Technique ◽  
Chsh Inequalities

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a nonlinear entanglement witness and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.

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