701 research outputs found
Surface Entanglement in Quantum Spin Networks
We study the ground-state entanglement in systems of spins forming the
boundary of a quantum spin network in arbitrary geometries and dimensionality.
We show that as long as they are weakly coupled to the bulk of the network, the
surface spins are strongly entangled, even when distant and non directly
interacting, thereby generalizing the phenomenon of long-distance entanglement
occurring in quantum spin chains. Depending on the structure of the couplings
between surface and bulk spins, we discuss in detail how the patterns of
surface entanglement can range from multi-pair bipartite to fully multipartite.
In the context of quantum information and communication, these results find
immediate application to the implementation of quantum routers, that is devices
able to distribute quantum correlations on demand among multiple network nodes.Comment: 8 pages, 8 figure
Frustration, Entanglement, and Correlations in Quantum Many Body Systems
We derive an exact lower bound to a universal measure of frustration in
degenerate ground states of quantum many-body systems. The bound results in the
sum of two contributions: entanglement and classical correlations arising from
local measurements. We show that average frustration properties are completely
determined by the behavior of the maximally mixed ground state. We identify
sufficient conditions for a quantum spin system to saturate the bound, and for
models with twofold degeneracy we prove that average and local frustration
coincide.Comment: 9 pages, 1 figur
Dymanics of Generalized Coherent States
We show that generalized coherent states follow Schr\"{o}dinger dynamics in
time-dependent potentials. The normalized wave-packets follow a classical
evolution without spreading; in turn, the Schr\"{o}dinger potential depends on
the state through the classical trajectory. This feedback mechanism with
continuous dynamical re-adjustement allows the packets to remain coherent
indefinetely.Comment: 8 pages, plain latex, no figure
Discord of response
The presence of quantum correlations in a quantum state is related to the
state response to local unitary perturbations. Such response is quantified by
the distance between the unperturbed and perturbed states, minimized with
respect to suitably identified sets of local unitary operations. In order to be
a bona fide measure of quantum correlations, the distance function must be
chosen among those that are contractive under completely positive and trace
preserving maps. The most relevant instances of such physically well behaved
metrics include the trace, the Bures, and the Hellinger distance. To each of
these metrics one can associate the corresponding discord of response, namely
the trace, or Hellinger, or Bures minimum distance from the set of unitarily
perturbed states. All these three discords of response satisfy the basic axioms
for a proper measure of quantum correlations. In the present work we focus in
particular on the Bures distance, which enjoys the unique property of being
both Riemannian and contractive under completely positive and trace preserving
maps, and admits important operational interpretations in terms of state
distinguishability. We compute analytically the Bures discord of response for
two-qubit states with maximally mixed marginals and we compare it with the
corresponding Bures geometric discord, namely the geometric measure of quantum
correlations defined as the Bures distance from the set of classically
correlated quantum states. Finally, we investigate and identify the maximally
quantum correlated two-qubit states according to the Bures discord of response.
These states exhibit a remarkable nonlinear dependence on the global state
purity.Comment: 10 pages, 2 figures. Improved and expanded version, to be published
in J. Phys. A: Math. Ge
Theory of ground state factorization in quantum cooperative systems
We introduce a general analytic approach to the study of factorization points
and factorized ground states in quantum cooperative systems. The method allows
to determine rigorously existence, location, and exact form of separable ground
states in a large variety of, generally non-exactly solvable, spin models
belonging to different universality classes. The theory applies to
translationally invariant systems, irrespective of spatial dimensionality, and
for spin-spin interactions of arbitrary range.Comment: 4 pages, 1 figur
Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: from superfluidity to density waves
For systems of interacting, ultracold spin-zero neutral bosonic atoms,
harmonically trapped and subject to an optical lattice potential, we derive an
Extended Bose Hubbard (EBH) model by developing a systematic expansion for the
Hamiltonian of the system in powers of the lattice parameters and of a scale
parameter, the {\it lattice attenuation factor}. We identify the dominant terms
that need to be retained in realistic experimental conditions, up to
nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the
on site occupation numbers. In mean field approximation, we determine the free
energy of the system and study the phase diagram both at zero and at finite
temperature. At variance with the standard on site Bose Hubbard model, the zero
temperature phase diagram of the EBH model possesses a dual structure in the
Mott insulating regime. Namely, for specific ranges of the lattice parameters,
a density wave phase characterizes the system at integer fillings, with domains
of alternating mean occupation numbers that are the atomic counterparts of the
domains of staggered magnetizations in an antiferromagnetic phase. We show as
well that in the EBH model, a zero-temperature quantum phase transition to pair
superfluidity is in principle possible, but completely suppressed at lowest
order in the lattice attenuation factor. Finally, we determine the possible
occurrence of the different phases as a function of the experimentally
controllable lattice parameters.Comment: 18 pages, 7 figures, accepted for publication in Phys. Rev.
Controllable Gaussian-qubit interface for extremal quantum state engineering
We study state engineering through bilinear interactions between two remote
qubits and two-mode Gaussian light fields. The attainable two-qubit states span
the entire physically allowed region in the entanglement-versus-global-purity
plane. Two-mode Gaussian states with maximal entanglement at fixed global and
marginal entropies produce maximally entangled two-qubit states in the
corresponding entropic diagram. We show that a small set of parameters
characterizing extremally entangled two-mode Gaussian states is sufficient to
control the engineering of extremally entangled two-qubit states, which can be
realized in realistic matter-light scenarios.Comment: 4+3 pages, 6 figures, RevTeX4. Close to published version with
appendi
Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions
Frustration in quantum many body systems is quantified by the degree of
incompatibility between the local and global orders associated, respectively,
to the ground states of the local interaction terms and the global ground state
of the total many-body Hamiltonian. This universal measure is bounded from
below by the ground-state bipartite block entanglement. For many-body
Hamiltonians that are sums of two-body interaction terms, a further inequality
relates quantum frustration to the pairwise entanglement between the
constituents of the local interaction terms. This additional bound is a
consequence of the limits imposed by monogamy on entanglement shareability. We
investigate the behavior of local pair frustration in quantum spin models with
competing interactions on different length scales and show that valence bond
solids associated to exact ground-state dimerization correspond to a transition
from generic frustration, i.e. geometric, common to classical and quantum
systems alike, to genuine quantum frustration, i.e. solely due to the
non-commutativity of the different local interaction terms. We discuss how such
frustration transitions separating genuinely quantum orders from classical-like
ones are detected by observable quantities such as the static structure factor
and the interferometric visibility.Comment: 11 pages, 7 figures. Matches published versio
Diffusion Processes and Coherent States
It is shown that stochastic processes of diffusion type possess, in all
generality, a structure of uncertainty relations and of coherent and squeezed
states. This fact is used to obtain, via Nelson stochastic formulation of
quantum mechanics, the harmonic-oscillator coherent and squeezed states. The
method allows to derive new minimum uncertainty states in time-dependent
oscillator potentials and for the Caldirola-Kanai model of quantum damped
oscillator.Comment: 11 pages, plain LaTe
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
We present a general scheme for the study of frustration in quantum systems.
We introduce a universal measure of frustration for arbitrary quantum systems
and we relate it to a class of entanglement monotones via an exact inequality.
If all the (pure) ground states of a given Hamiltonian saturate the inequality,
then the system is said to be inequality saturating. We introduce sufficient
conditions for a quantum spin system to be inequality saturating and confirm
them with extensive numerical tests. These conditions provide a generalization
to the quantum domain of the Toulouse criteria for classical frustration-free
systems. The models satisfying these conditions can be reasonably identified as
geometrically unfrustrated and subject to frustration of purely quantum origin.
Our results therefore establish a unified framework for studying the
intertwining of geometric and quantum contributions to frustration.Comment: 8 pages, 1 figur
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