Monotones and invariants for multi-particle quantum states

H Barnum, N Linden

Research output: Contribution to journalArticle (Academic Journal)peer-review

214 Citations (Scopus)

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.
Translated title of the contributionMonotones and invariants for multi-particle quantum states
Original languageEnglish
Pages (from-to)6787 - 6805
JournalJournal of Physics A: Mathematical and General
Volume34 (35)
Publication statusPublished - 7 Sept 2001

Bibliographical note

Publisher: IOP Publishing Ltd
Other identifier: IDS number 481VG

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