Exploring degrees of entanglement

Exploring degrees of entanglement In spite of a long history, the quantification of entanglement still calls for exploration. What matters about entanglement depends on the situation, and so presumably do the numbers suitable for its quantification. Regardless of situational complications, a necessary first step is to make available for calculation some quantitative measure of entanglement. Here we define a geometric degree of entanglement, distinct from earlier definitions, but in the case of bipartite pure states related to that proposed by Shimony (Ann N Y Acad Sci 755:675–679, 1995). The definition offered here applies also to multipartite mixed states, and a variational method simplifies the calculation. We analyze especially states that are invariant under permutation of particles, states that we call bosonic. Of interest to quantum sensing, for bosonic states, we show that no partial trace can increase a degree of entanglement. For some sample cases we quantify the degree of entanglement surviving a partial trace. As a function of the degree of entanglement of a bosonic 3-qubit pure state, we show the range of degree of entanglement for the 2-qubit reduced density matrix obtained from it by a partial trace. Then we calculate an upper bound on the degree of entanglement of the mixed state obtained as a partial trace over one qubit of a 4-qubit bosonic state. As a reminder of the situational dependence of the advantage of entanglement, we review the way in which entanglement combines with scattering theory in the example of light-based radar. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Exploring degrees of entanglement

Loading next page...
Springer US
Copyright © 2009 by Springer Science+Business Media, LLC
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial