AUTHORS: Iulia Ghiu1), 2),
Mohamed Bourennane1), and Anders Karlsson1)
1) Department of Microelectronics and Information Technology, Royal
Institute of
Technology (KTH), Electrum 229, 164 40 Kista, Sweden;
2) Department of Physics, Laboratory of Statistical Physics and Quantum
Mechanics, University of Bucharest, PO Box MG-11, R-76900,
Bucharest- Magurele,
Romania.
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ABSTRACT:
Entanglement is the key physical resource in most quantum information
processes,
e.g. quantum teleportation, two- or multiparty quantum cryptography, and
quantum computation.
Moving onwards from two-particle entangled states, much interest has been
devoted to three-particle entangled states, notably the Greenberger-Horne-Zeilinger
(GHZ) states and their role in generalizations of Bell inequalities, as well as an enabling
resource for quantum computation.
Whereas for two-particle states, entanglement local manipulation is known,
for three or multiparticle entanglement, there still remain unresolved issues
concerning both
entanglement transformations as well as possible applications in quantum
information processing.
Recently, it was shown [1] that three-particle entangled states of the
GHZ-type and of the W-type are inequivalent in the following sense: if we allow only
Stochastic Local quantum Operations and Classical Communications [2], abbreviated SLOCC, then one
cannot succeed in transforming states from the GHZ-class to the W-class and vice-versa with
a non-zero probability of success. Of some interest in entanglement transformations
has been entanglement catalysis process. The questions we address here are: Can we
perform the transformation between the two inequivalent classes using a catalysis
state, such as shared Einstein-Podolsky-Rosen (EPR) pairs, and which is the maximal probability
of success to transform W-states into GHZ-states and vice-versa by using SLOCC in
presence of additional entanglement resources?
We show that a catalysis procedure between W-states and GHZ-states using
either a
non-maximally entangled bipartite state, GHZ or W-states as catalysis
states is not possible. Then we find the optimal protocol for conversion of a certain
family of the
W-states and an EPR pair into the state GHZ [3].
REFERENCES:
[1] W. Dur, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
[2] C.H. Bennett, S. Popescu, D. Rohrlich, J.A. Smolin, and A.V.
Thapiliyal,
Phys. Rev. A 63, 012307 (2001).
[3] I. Ghiu, M. Bourennane, and A. Karlsson, Phys. Lett. A 287, 12 (2001).
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