Hierarchies of geometric entanglement

M. Blasone, F. Dell’Anno, S. De Siena, and F. Illuminati
Phys. Rev. A 77, 062304 – Published 3 June 2008

Abstract

We introduce a class of generalized geometric measures of entanglement. For pure quantum states of N elementary subsystems, they are defined as the distances from the sets of K-separable states (K=2,,N). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows discrimination among the different contributions. The extended measures are applied to the study of entanglement in different classes of N-qubit pure states. These classes include W and Greenberger-Horne-Zeilinger (GHZ) states, and their symmetric superpositions; symmetric multimagnon states; cluster states; and, finally, asymmetric generalized W-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and W states, clarifying the original result of Wei and Goldbart that W states possess a larger global entanglement than GHZ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 December 2007

DOI:https://doi.org/10.1103/PhysRevA.77.062304

©2008 American Physical Society

Authors & Affiliations

M. Blasone1,2, F. Dell’Anno1,2,3,4, S. De Siena1,2,3,4, and F. Illuminati1,2,3,4,5,*

  • 1Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
  • 2Gruppo Collegato di Salerno, INFN Sezione di Napoli, Salerno, Italy
  • 3CNR-INFM Coherentia, Napoli, Italy
  • 4CNISM Unità di Salerno, Salerno, Italy
  • 5ISI Foundation for Scientific Interchange, Viale Settimio Severo 65, 00173 Torino, Italy

  • *Corresponding author. illuminati@sa.infn.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 77, Iss. 6 — June 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×