Prime decomposition and correlation measure of finite quantum systems
Ellinas, D. ; Floratos, E. G.
arXiv, 9806007 / Harvested from arXiv
Text on arXiv
Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of density matrices a complete tensor product factorization is achieved. The construction is based on the Chinese Remainder Theorem and the projective unitary representation of $Z_N$ by the discrete Heisenberg group $H_N$. The pd isomorphism is unitarily implemented and it is shown to be coassociative and to act on $H_N$ as comultiplication. Density matrices with complete pd are interpreted as grouplike elements of $H_N$. To quantify the distance of $\rho$ from its pd a trace-norm correlation index $\cal E$ is introduced and its invariance groups are determined.
Publié le : 1998-06-02
Classification:  Quantum Physics,  Mathematical Physics,  Mathematics - Quantum Algebra 
@article{9806007,
     author = {Ellinas, D. and Floratos, E. G.},
     title = {Prime decomposition and correlation measure of finite quantum systems},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9806007}
}

Ellinas, D.; Floratos, E. G. Prime decomposition and correlation measure of finite quantum systems. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9806007/