scholarly journals Deformed Entropic and Information Inequalities forX-States of Two-Qubit and Single Qudit States

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
V. I. Man’ko ◽  
L. A. Markovich
Keyword(s):  
The State ◽  
Entropic Inequalities ◽  
Classical Systems ◽  
Information Inequalities ◽  
Qubit System ◽  
Single Qudit ◽  
Entropic And Information Inequalities

Theq-deformed entropies of quantum and classical systems are discussed. Standard andq-deformed entropic inequalities forX-states of the two-qubit system and the state of single qudit withj=3/2are presented.

scholarly journals The fundamental connections between classical Hamiltonian mechanics, quantum mechanics and information entropy

2020 ◽  
Vol 18 (01) ◽  
pp. 1941025
Author(s):  
Gabriele Carcassi ◽  
Christine A. Aidala
Keyword(s):  
Quantum Mechanics ◽  
Information Entropy ◽  
Quantum Systems ◽  
The State ◽  
Hamiltonian Mechanics ◽  
Internal Dynamics ◽  
Classical Systems ◽  
Arbitrary Precision

We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to understand the analogies and differences between the two theories.

Entanglement and other quantum correlations of a single qudit state

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560006 ◽  
Author(s):  
Margarita A. Man'ko ◽  
Vladimir I. Man'ko
Keyword(s):  
Quantum Computing ◽  
Quantum Communication ◽  
Quantum Correlations ◽  
Arbitrary Spin ◽  
Entropic Inequalities ◽  
Strong Subadditivity ◽  
Subadditivity Condition ◽  
New Information ◽  
Single Qudit ◽  
Information And Entropic Inequalities

The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.

scholarly journals New Minkowski type inequalities and entropic inequalities for quantum states of qudits

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560021 ◽  
Author(s):  
V. I. Man'ko ◽  
L. A. Markovich
Keyword(s):  
Quantum System ◽  
Quantum States ◽  
System State ◽  
Entropic Inequalities ◽  
Information Inequality ◽  
Strong Subadditivity ◽  
Subadditivity Condition ◽  
Composite Quantum System ◽  
Single Qudit ◽  
Two Parameter

The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian non-negative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for density matrix of noncomposite finite quantum system, e.g. for a single qudit state. The analogs of strong subadditivity condition for the single qudit is discussed in context of obtained Minkowski like inequality.

L-S decomposition for 2x2 density matrix by using Wootters's basis

2003 ◽  
Vol 3 (3) ◽  
pp. 229-248
Author(s):  
S.J. Akhtarshenas ◽  
M.A. Jafarizadeh
Keyword(s):  
Density Matrix ◽  
Hermitian Matrix ◽  
Full Rank ◽  
The State ◽  
Separable State ◽  
Von Neumann ◽  
Quantum Operations ◽  
Qubit System ◽  
Unitary Transformations ◽  
Local Quantum

An analytical expression for optimal Lewenstein-Sanpera (L-S) decomposition of a generic two qubit density matrix is given. By evaluating the L-S decomposition of Bell decomposable states, the optimal decomposition for arbitrary full rank state of two qubit system is obtained via local quantum operations and classical communications (LQCC). In Bell decomposable case the separable state optimizing L-S decomposition, minimize the von Neumann relative entropy as a measure of entanglement. The L-S decomposition for a generic two-qubit density matrix is only obtained by using Wootters's basis. It is shown that the average concurrence of the decomposition is equal to the concurrence of the state. It is also shown that all the entanglement content of the state is concentrated in the Wootters's state |x_1> associated with the largest eigenvalue \lambda_1 of the Hermitian matrix \sqrt{\sqrt{rho}\tilde{rho}\sqrt{rho}} . It is shown that a given density matrix rho with corresponding set of positive numbers \lambda_i and Wootters's basis can transforms under SO(4,c) into a generic 2x2 matrix with the same set of positive numbers but with new Wootters's basis, where the local unitary transformations correspond to SO(4,r) transformations, hence, \rho can be represented as coset space SO(4,c)/SO(4,r) together with positive numbers lambda_i.

Practical Picture Processing

1974 ◽  
Vol 32 ◽  
pp. 338-339
Author(s):  
T. A. Welton
Keyword(s):  
Radiation Damage ◽  
Coherence Length ◽  
Spatial Information ◽  
State Of The Art ◽  
Coherent Radiation ◽  
The State ◽  
Energy Spread ◽  
Electron Micrograph ◽  
Picture Processing ◽  
Molecular Skeleton

Various authors have emphasized the spatial information resident in an electron micrograph taken with adequately coherent radiation. In view of the completion of at least one such instrument, this opportunity is taken to summarize the state of the art of processing such micrographs. We use the usual symbols for the aberration coefficients, and supplement these with £ and 6 for the transverse coherence length and the fractional energy spread respectively. He also assume a weak, biologically interesting sample, with principal interest lying in the molecular skeleton remaining after obvious hydrogen loss and other radiation damage has occurred.

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