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Journal of Applied Mathematics and Physics

About Factorization of Quantum States with Few Qubits

Gustavo V. López, Gustavo Montes, Manuél Ávila, Juvenal Rueda-Paz

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Through the study of the factorization conditions of a wave function made up of two, three and four qubits, we propose an analytical expression which can characterize entangled states in terms of the coefficients of the wave function and density matrix elements.
DOI
10.4236/jamp.2017.52042

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Matrix elements of two-body operators between many-particle permutational symmetry-adapted functions in hyperspherical coordinates are constructed. The matrix elements are evaluated using the appropriate hyperspherical coefficients of fractional parentage, the Raynal-Revai coefficients, and the hyperspherical recoupling coefficients. We use the power expansion of the two-body operators and obtain an analytic expression for the matrix element of each term. These expressions are studied numerically. The results allow precise evaluations of two-body matrix elements for few-body calculations in nuclear, atomic, and molecular physics.