Quantum Information Processing, Vol. 6, No. 5, October 2007 (© 2007)
Nonlinear Response and Observable Signatures
of Equilibrium Entanglement
A. M. Zagoskin,
A. Yu. Smirnov,
S. K. Gupta,
and I. S. Slobodov
Received March 26, 2007; accepted July 27, 2007; Published online: September 19, 2007
We investigate how equilibrium entanglement is manifested in the nonlinear
response of an N -qubit system. We show that in the thermodynamic limit the
irreducible part of the nth-order nonlinear susceptibility indicates that the eigen-
states of the system contain entangled (n + 1)-qubit clusters. This opens the way
to a directly observable multiqubit entanglement signature. We show that the irre-
ducible part of the static cubic susceptibility of a system of four ﬂux qubits,
as a function of external parameters, behaves as a global 4-qubit entanglement
measure introduced in Ref. (20). We discuss the possibility of extracting purely-
entanglement-generated contribution from the general multipoint correlators in a
KEY WORDS: multiqubit entanglement; nonlinear susceptibility.
PACS: 03.67.Mn; 03.67.Lx; 05.30-d.
The “equilibrium”, or “thermodynamic”, entanglement in spin systems is
a quantiﬁcation of the degree of non-classicality of the eigenstates of the
system (e.g. Refs. (1–5)). In quantum phase transitions it can be regarded
as a speciﬁc order parameter.
It distinguishes between the classical cor-
relations, produced by interaction, and the purely quantum ones. Both
types of correlations are contained in multi-point Greens’ functions of the
Department of Physics and Astronomy, The University of British Columbia, Vancouver,
BC, Canada V6T 1Z1.
Digital Materials Lab., Frontier Research System, RIKEN, 2-1 Hirosawa, Wako-shi,
Saitama 351-0198, Japan.
CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan.
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
1570-0755/07/1000-0381/0 © 2007 Springer Science+Business Media, LLC