Monotones and invariants for multi-particle quantum states

@article{citeulike:1126044, abstract = {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.}, author = {Barnum, H. and Linden, N. }, citeulike-article-id = {1126044}, doi = {http://dx.doi.org/10.1088/0305-4470/34/35/305}, journal = {Journal of Physics A: Mathematical and General}, keywords = {invariant, monotone, n-partite}, number = {35}, pages = {6787--6805}, posted-at = {2007-02-27 08:24:53}, priority = {3}, title = {Monotones and invariants for multi-particle quantum states}, url = {http://dx.doi.org/10.1088/0305-4470/34/35/305}, volume = {34}, year = {2001} }

TY - JOUR ID - citeulike:1126044 L3 - citeulike-article-id:1126044 TI - Monotones and invariants for multi-particle quantum states JF - Journal of Physics A: Mathematical and General VL - 34 IS - 35 SP - 6787 EP - 6805 N2 - 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. KW - invariant KW - monotone KW - n-partite AU - Barnum, H AU - Linden, N PY - 2001/// UR - http://dx.doi.org/10.1088/0305-4470/34/35/305 ER -