scholarly journals CLASSICALITY WITNESS FOR TWO-QUBIT STATES

2012 ◽  
Vol 10 (03) ◽  
pp. 1250028 ◽  
Author(s):  
JONAS MAZIERO ◽  
ROBERTO M. SERRA
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Probability Distribution ◽  
Quantum Discord ◽  
Orthonormal Basis ◽  
Broad Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Classical Correlations ◽  
Necessary And Sufficient ◽  
Qubit States

In the last few years one realized that if the state of a bipartite system can be written as ∑i,j pij|ai〉〈ai| ⊗ |bj〉〈bj|, where {|ai〉} and {|bj〉} form orthonormal basis for the subsystems and {pij} is a probability distribution, then it possesses at most classical correlations. In this article we introduce a nonlinear witness providing a sufficient condition for classicality of correlations (absence of quantum discord) in a broad class of two-qubit systems. Such witness turns out to be necessary and sufficient condition in the case of Bell-diagonal states. We show that the witness introduced here can be readily experimentally implemented in nuclear magnetic resonance setups.

scholarly journals Isometric Signal Processing under Information Geometric Framework

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 332 ◽  
Author(s):  
Hao Wu ◽  
Yongqiang Cheng ◽  
Hongqiang Wang
Keyword(s):  
Signal Processing ◽  
Probability Distribution ◽  
Geometric Structure ◽  
Information Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Statistical Manifold ◽  
Intrinsic Parameter ◽  
Geometric Framework ◽  
Necessary And Sufficient

Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

Orthogonal Fractional Factorial Plans

1980 ◽  
Vol 29 (3-4) ◽  
pp. 143-160 ◽  
Author(s):  
Rahul Mukerjee
Keyword(s):  
Broad Class ◽  
Existence Results ◽  
Fractional Factorial ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equal Frequency ◽  
Other Hand ◽  
Necessary And Sufficient ◽  
Generally True

This paper shows that the criterion of proportional frequency for (unblocked) orthogonal fractional factorial plans, as suggested by some previous authors, is not generally true. On the other hand, the criterion of equal frequency has been established as a necessary and sufficient condition in the general case. Some other properties of orthogonal fractional factorial plans have been investigated. A necessary and sufficient condition for designs involving two or more blocks has also been presented. A broad class of non-existence results follow.

A characterization of the exponential distribution

1972 ◽  
Vol 9 (02) ◽  
pp. 457-461 ◽  
Author(s):  
M. Ahsanullah ◽  
M. Rahman
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Lebesgue Measure ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Random Variable ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

Vector-valued nonuniform multiresolution analysis on local fields

2015 ◽  
Vol 13 (04) ◽  
pp. 1550029 ◽  
Author(s):  
Firdous Ahmad Shah ◽  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Orthonormal Basis ◽  
Positive Characteristic ◽  
Local Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Vilenkin Groups ◽  
Refinement Mask ◽  
Necessary And Sufficient ◽  
Vector Valued

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 𝒵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 𝒵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups.

scholarly journals Necessary and Sufficient Condition for Stability of Generalized Expectation Value

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Aziz El Kaabouchi ◽  
Sumiyoshi Abe
Keyword(s):  
Probability Distribution ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Nonequilibrium Statistical Mechanics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Expectation Value ◽  
Necessary And Sufficient ◽  
Small Deformations ◽  
Generalized Expectation

A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution.

scholarly journals A class of simple tracially AFC*-algebras

2002 ◽  
Vol 31 (5) ◽  
pp. 271-282
Author(s):  
N. E. Livingston
Keyword(s):  
Inductive Limit ◽  
Broad Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The concept of a tracially AF (TAF)C*-algebra was introduced recently to aid in the classification of nuclearC*-algebrasHere, we construct and study a broad class of inductive-limitC*-algebras. We give a numerical condition which, when satisfied, ensures that the corresponding algebra in our construction has the TAF property. We further give a necessary and sufficient condition under which certain of theseC*-algebras are TAF.

The linear stochastic heat equation with Hermite noise

2019 ◽  
Vol 22 (03) ◽  
pp. 1950022 ◽  
Author(s):  
Meryem Slaoui ◽  
C. A. Tudor
Keyword(s):  
Probability Distribution ◽  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Self Similarity ◽  
Wiener Chaos ◽  
Sample Paths ◽  
Non Gaussian ◽  
Necessary And Sufficient

We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order [Formula: see text]. This solution is an element of the [Formula: see text]th Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, [Formula: see text]-variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when [Formula: see text].

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