Quantum Information Processing, Vol. 6, No. 5, October 2007 (© 2007)
GHZ States, Almost-Complex Structure
and Yang–Baxter Equation
and Mo-Lin Ge
Received February 14, 2007; accepted June 7, 2007; Published online: September 21, 2007
Recent research suggests that there are natural connections between quantum
information theory and the Yang–Baxter equation. In this paper, in terms of
the almost-complex structure and with the help of its algebra, we deﬁne the
Bell matrix to yield all the Greenberger–Horne–Zeilinger (GHZ) states from the
product basis, prove it to form a unitary braid representation and presents a new
type of solution of the quantum Yang–Baxter equation. We also study Yang–
Baxterization, Hamiltonian, projectors, diagonalization, noncommutative geome-
try, quantum algebra and FRT dual algebra associated with this generalized Bell
KEY WORDS: GHZ state; Yang–Baxter; almost-complex structure; FRT.
PACS: 02.10.Kn; 03.65.Ud; 03.67.Lx.
Recently, a series of papers
have suggested there are natural and
deep connections between quantum information theory
and the Yang–
Baxter equation (YBE).
Unitary solutions of the braided YBE (i.e.,
the braid group relation)
as well as unitary solutions of the quan-
tum Yang–Baxter equation (QYBE)
can be often identiﬁed with uni-
versal quantum gates.
is exploited to set up the
odinger equation determining the unitary evolution of a unitary braid
Furthermore, the Werner state
is viewed as a rational solution
of the QYBE and the isotropic state
with a speciﬁc parameter forms a
Department of Physics, University of Utah, 115 S, 1400 E, Room 201, Salt Lake City, UT
84112-0830, USA. E-mail: email@example.com
Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin
300071, P.R. China. E-mail: firstname.lastname@example.org
To whom correspondence should be addressed.
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