Are General Quantum Correlations Monogamous?
Abstract
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.
 Publication:

Physical Review Letters
 Pub Date:
 August 2012
 DOI:
 10.1103/PhysRevLett.109.050503
 arXiv:
 arXiv:1112.3967
 Bibcode:
 2012PhRvL.109e0503S
 Keywords:

 03.67.a;
 Quantum information;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Physics  Computational Physics
 EPrint:
 5 pages, 1 figure, added a discussion of our main result in relation to the fact that separable states are infinitely shareable