scholarly journals Explicit constructions of all separable two-qubits density matrices and related problems for three-qubits systems

2015 ◽  
Vol 13 (08) ◽  
pp. 1550061 ◽  
Author(s):  
Y. Ben-Aryeh ◽  
A. Mann
Keyword(s):  
Pure State ◽  
State Density ◽  
Singular Value ◽  
High Order ◽  
Sufficient Condition ◽  
Lorentz Transformations ◽  
Density Matrices ◽  
Single Qubit ◽  
Pauli Matrices ◽  
Singular Value Decompositions

Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert–Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced to 3 by using local rotations, and for two-qubits states which include single qubit measurements, the number of parameters is reduced to 4 by local Lorentz transformations. For both cases, we related the absolute values of the HS parameters to probabilities, and the outer products of various Pauli matrices were transformed to pure state density matrices products. We discuss related problems for three-qubits. For n-qubits correlation systems ([Formula: see text]) the sufficient condition for separability may be improved by local transformations, related to high order singular value decompositions (SVDs).

Direct Determination of Pure-State Density Matrices. II. Construction of Constrained Idempotent One-Body Densities

1969 ◽  
Vol 177 (1) ◽  
pp. 7-13 ◽  
Author(s):  
William L. Clinton ◽  
Anthony J. Galli ◽  
Louis J. Massa
Keyword(s):  
Pure State ◽  
Direct Determination ◽  
State Density ◽  
Density Matrices

Direct Determination of Pure-State Density Matrices. V. Constrained Eigenvalue Problems

1969 ◽  
Vol 177 (1) ◽  
pp. 27-33 ◽  
Author(s):  
William L. Clinton ◽  
Anthony J. Galli ◽  
George A. Henderson ◽  
Guillermo B. Lamers ◽  
Louis J. Massa ◽  
...  
Keyword(s):  
Pure State ◽  
Eigenvalue Problems ◽  
Direct Determination ◽  
State Density ◽  
Density Matrices

Direct Determination of Pure-State Density Matrices. I. Some Simple Introductory Calculations

1969 ◽  
Vol 177 (1) ◽  
pp. 1-6 ◽  
Author(s):  
William L. Clinton ◽  
Jamil Nakhleh ◽  
Francis Wunderlich
Keyword(s):  
Pure State ◽  
Direct Determination ◽  
State Density ◽  
Density Matrices

scholarly journals Entanglement of formation and monogamy of multi-party quantum entanglement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeong San Kim
Keyword(s):  
Mutual Information ◽  
Quantum Entanglement ◽  
Pure State ◽  
Party Systems ◽  
Sufficient Condition ◽  
Density Matrices ◽  
Entanglement Of Formation ◽  
Classical Quantum ◽  
Arbitrary Dimensions ◽  
Reduced Density

AbstractWe provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical–classical–quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems of arbitrary dimensions.

scholarly journals Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators

2001 ◽  
Vol 8 (2) ◽  
pp. 323-332
Author(s):  
A. Meskhi
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators ◽  
Integral Transforms ◽  
Singular Value ◽  
Entropy Numbers ◽  
Liouville Type ◽  
Singular Value Decompositions

Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.

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