12 research outputs found
Interplay between computable measures of entanglement and other quantum correlations
Composite quantum systems can be in generic states characterized not only by
entanglement, but also by more general quantum correlations. The interplay
between these two signatures of nonclassicality is still not completely
understood. In this work we investigate this issue focusing on computable and
observable measures of such correlations: entanglement is quantified by the
negativity N, while general quantum correlations are measured by the
(normalized) geometric quantum discord D_G. For two-qubit systems, we find that
the geometric discord reduces to the squared negativity on pure states, while
the relationship holds for arbitrary mixed states. The latter
result is rigorously extended to pure, Werner and isotropic states of two-qudit
systems for arbitrary d, and numerical evidence of its validity for arbitrary
states of a qubit and a qutrit is provided as well. Our results establish an
interesting hierarchy, that we conjecture to be universal, between two relevant
and experimentally friendly nonclassicality indicators. This ties in with the
intuition that general quantum correlations should at least contain and in
general exceed entanglement on mixed states of composite quantum systems.Comment: 10 pages, 4 figure
Classical Tensors and Quantum Entanglement II: Mixed States
Invariant operator-valued tensor fields on Lie groups are considered. These
define classical tensor fields on Lie groups by evaluating them on a quantum
state. This particular construction, applied on the local unitary group
U(n)xU(n), may establish a method for the identification of entanglement
monotone candidates by deriving invariant functions from tensors being by
construction invariant under local unitary transformations. In particular, for
n=2, we recover the purity and a concurrence related function (Wootters 1998)
as a sum of inner products of symmetric and anti-symmetric parts of the
considered tensor fields. Moreover, we identify a distinguished entanglement
monotone candidate by using a non-linear realization of the Lie algebra of
SU(2)xSU(2). The functional dependence between the latter quantity and the
concurrence is illustrated for a subclass of mixed states parametrized by two
variables.Comment: 23 pages, 4 figure
Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
We study the distribution of the Schmidt coefficients of the reduced density
matrix of a quantum system in a pure state. By applying general methods of
statistical mechanics, we introduce a fictitious temperature and a partition
function and translate the problem in terms of the distribution of the
eigenvalues of random matrices. We investigate the appearance of two phase
transitions, one at a positive temperature, associated to very entangled
states, and one at a negative temperature, signalling the appearance of a
significant factorization in the many-body wave function. We also focus on the
presence of metastable states (related to 2-D quantum gravity) and study the
finite size corrections to the saddle point solution.Comment: 23 pages, 32 figures. More details added about the metastable branch
and the first-order phase transitio
Classical Tensors and Quantum Entanglement I: Pure States
The geometrical description of a Hilbert space asociated with a quantum
system considers a Hermitian tensor to describe the scalar inner product of
vectors which are now described by vector fields. The real part of this tensor
represents a flat Riemannian metric tensor while the imaginary part represents
a symplectic two-form. The immersion of classical manifolds in the complex
projective space associated with the Hilbert space allows to pull-back tensor
fields related to previous ones, via the immersion map. This makes available,
on these selected manifolds of states, methods of usual Riemannian and
symplectic geometry. Here we consider these pulled-back tensor fields when the
immersed submanifold contains separable states or entangled states. Geometrical
tensors are shown to encode some properties of these states. These results are
not unrelated with criteria already available in the literature. We explicitly
deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy
Classical Statistical Mechanics Approach to Multipartite Entanglement
We characterize the multipartite entanglement of a system of n qubits in
terms of the distribution function of the bipartite purity over balanced
bipartitions. We search for maximally multipartite entangled states, whose
average purity is minimal, and recast this optimization problem into a problem
of statistical mechanics, by introducing a cost function, a fictitious
temperature and a partition function. By investigating the high-temperature
expansion, we obtain the first three moments of the distribution. We find that
the problem exhibits frustration.Comment: 38 pages, 10 figures, published versio