Symmetric extension of twoqubit states
Abstract
A bipartite state ρ_{AB} is symmetric extendible if there exists a tripartite state ρ_{A}BB' whose AB and A^{B'} marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, oneway distillation of EinsteinPodolskyRosen pairs, oneway distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any twoqubit quantum state ρ_{AB}; specifically, tr(ρ_{B}^{2})≥tr(ρA_{B}^{2})4√ detρ_{AB} . As a special case we solve the bosonic threerepresentability problem for the twobody reduced density matrix.
 Publication:

Physical Review A
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevA.90.032318
 arXiv:
 arXiv:1310.3530
 Bibcode:
 2014PhRvA..90c2318C
 Keywords:

 03.67.Mn;
 03.65.Ud;
 03.67.Dd;
 Entanglement production characterization and manipulation;
 Entanglement and quantum nonlocality;
 Quantum cryptography;
 Quantum Physics
 EPrint:
 10 pages, no figure. comments are welcome. Version 2: introduction rewritten