# Geometric discord and measurement-induced nonlocality for well known bound entangled states

Geometric discord and measurement-induced nonlocality for well known bound entangled states We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ( $$2\otimes 4, 3\otimes 3$$ and $$4\otimes 4$$ dimensional) bound entangled states and that of Bennett et al.’s in $$3\otimes 3$$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $$4\otimes 4$$ bound entangled state of Benatti et al. and the $$2\otimes 8$$ state having the same matrix representation (in computational basis) is same. Coincidently, the $$2m\otimes 2m$$ Werner and isotropic states also exhibit the same property, when seen as $$2\otimes 2m^2$$ dimensional states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Geometric discord and measurement-induced nonlocality for well known bound entangled states

, Volume 12 (7) – Feb 23, 2013
12 pages

/lp/springer_journal/geometric-discord-and-measurement-induced-nonlocality-for-well-known-swlUeRRhld
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0545-5
Publisher site
See Article on Publisher Site

### Abstract

We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ( $$2\otimes 4, 3\otimes 3$$ and $$4\otimes 4$$ dimensional) bound entangled states and that of Bennett et al.’s in $$3\otimes 3$$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $$4\otimes 4$$ bound entangled state of Benatti et al. and the $$2\otimes 8$$ state having the same matrix representation (in computational basis) is same. Coincidently, the $$2m\otimes 2m$$ Werner and isotropic states also exhibit the same property, when seen as $$2\otimes 2m^2$$ dimensional states.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 23, 2013

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