Fraction of isospectral states exhibiting quantum correlations
Abstract
For several types of correlations (mixedstate entanglement in systems of distinguishable particles, particle entanglement in systems of indistinguishable bosons and fermions, and nonGaussian correlations in fermionic systems) we estimate the fraction of noncorrelated states among the density matrices with the same spectra. We prove that for the purity exceeding some critical value (depending on the considered problem) fraction of noncorrelated states tends to zero exponentially fast with the dimension of the relevant Hilbert space. As a consequence, a state randomly chosen from the set of density matrices possessing the same spectra is asymptotically a correlated one. To prove this we developed a systematic framework for detection of correlations via nonlinear witnesses.
 Publication:

Physical Review A
 Pub Date:
 July 2014
 DOI:
 10.1103/PhysRevA.90.010302
 arXiv:
 arXiv:1312.7359
 Bibcode:
 2014PhRvA..90a0302O
 Keywords:

 03.67.Mn;
 02.20.Sv;
 03.65.Fd;
 Entanglement production characterization and manipulation;
 Lie algebras of Lie groups;
 Algebraic methods;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 7 pages, 1 figure, title changed, abstract and introduction rewritten, one reference added