Direct Determination of Pure-State Density Matrices. III. Purely Theoretical Densities Via an Electrostatic-Virial Theorem

1969 ◽  
Vol 177 (1) ◽  
pp. 13-18 ◽  
Author(s):  
William L. Clinton ◽  
George A. Henderson ◽  
John V. Prestia
Keyword(s):  
Pure State ◽  
Virial Theorem ◽  
Direct Determination ◽  
State Density ◽  
Density Matrices

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 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).

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