On the separability of unitarily invariant random quantum states  the unbalanced regime
Abstract
We study entanglementrelated properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1802.00067
 arXiv:
 arXiv:1802.00067
 Bibcode:
 2018arXiv180200067N
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 Quantum Physics
 EPrint:
 New section on PPT matrices with large Schmidt number