Andrew C. Doherty

Entanglement gap, monogamy of entanglement and quantum de Finetti theorems

I will discuss the concept of entanglement gap--- the difference between the ground-state energy and the minimum energy that a separable state may attain---for quantum many-body systems. In particular, as was shown in quant-ph/0408086, I will explain why a form of the monogamy of entanglement for mixed states requires that for bipartite spin lattices the entanglement gap necessarily decreases as the co-ordination number is increased. The key technical tool is a generalization of the quantum de Finetti theorem dating back to the eighties. I will show that a recent version of this theorem for a finite number of copies, due to Koenig and Renner (quant-ph/0410229), provides explicit bounds on the entanglement gap in terms of co-ordination number.