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Foundations of Physics

, Volume 29, Issue 4, pp 527–552 | Cite as

Multiparticle Entanglement

  • H. A. Carteret
  • N. Linden
  • S. Popescu
  • A. Sudbery
Article

Abstract

The Greenberger-Horne-Zeilinger state is the most famous example of a state with multiparticle entanglement. In this article we describe a group theoretic framework we have been developing for understanding the entanglement in general states of two or more quantum particles. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)n). We consider both pure and mixed states and calculate the number of independent parameters needed to describe such states up to this equivalence. We describe how the entanglement of states in a given equivalence class may be characterized by the stability group of the action of the group of local rotations on any of the states in the class. We also show how to calculate invariants under the group of local actions for both pure and mixed states. In the case of mixed states we are able to explicitly exhibit sets of invariants which allow one to determine whether two generic mixed states are equivalent up to local unitary transformations.

Keywords

General State Equivalence Class Mixed State Local Action Independent Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • H. A. Carteret
  • N. Linden
  • S. Popescu
  • A. Sudbery

There are no affiliations available

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