Quantum Information Processing, Vol. 4, No. 3, August 2005 (© 2005)
Reversibility of Local Transformations of Multiparticle
Received March 2, 2005; accepted March 21, 2005
We consider the transformation of multisystem entangled states by local quan-
tum operations and classical communication. We show that, for any reversible
transformation, the relative entropy of entanglement for any two parties must
remain constant. This shows, for example, that it is not possible to convert 2N
three-party GHZ states into 3N singlets, even in an asymptotic sense. Thus there
is true three-party non-locality (i.e. not all three party entanglement is equiva-
lent to two-party entanglement). Our results also allow us to make quantitative
statements about concentrating multi-particle entanglement. Finally, we show that
there is true n-party entanglement for any n.
KEY WORDS: Multiparticle entanglement; reversibility; local operations; rela-
This letter concerns the subject of quantum entanglement, a subject at the core
of the newly developed and rapidly changing ﬁelds of quantum information
and communication. Entanglement is also of great importance for founda-
tions of quantum mechanics, and many experimental branches of physics—
quantum optics, NMR, condensed matter—have shown increased interest.
One of the key open issues in quantum information theory is to
understand what the fundamentally different types of quantum entangle-
ment are. A quantum state ψ is considered to be equivalent to another
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
and BRIMS, Hewlett-Packard Laboratories, Stoke Gifford, Bristol BS12 6QZ, UK.
Department of Physics, Kenyon College, Gambier, OH 43022, USA.
Department of Mathematical Sciences, Denison University, Granville, OH 43023, USA.
1570-0755/05/0800-0241/0 © 2005 Springer Science+Business Media, Inc.