2001/03/28 by H. Barnum, N. Linden
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1088/0305-4470/34/35/305
25 pages, LaTeX
arxiv created 2001/03/28 · arxiv updated 2009/12/01
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication. These include restrictions which do not follow from any bipartite considerations. We derive supermultiplicativity relations between each state's monotones and the monotones for collective processing when the parties share several states. We also investigate polynomial invariants under local unitary transformations, and show that a large class of these are invariant under collective unitary processing and also multiplicative, putting restrictions, for example, on the exact conversion of multiple copies of one state to multiple copies of another.