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arXiv:quant-ph/0405049 · Journal of Physics A Mathematical and General

A bipartite class of entanglement monotones forN-qubit pure states

Clive Emary

Published Aug 12, 2004• 22 citations
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Abstract

We construct a class of algebraic invariants for N -qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well-known linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.
DOI
10.1088/0305-4470/37/34/008

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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.