683 research outputs found

### Bipartite and Multipartite Entanglement of Gaussian States

In this chapter we review the characterization of entanglement in Gaussian
states of continuous variable systems. For two-mode Gaussian states, we discuss
how their bipartite entanglement can be accurately quantified in terms of the
global and local amounts of mixedness, and efficiently estimated by direct
measurements of the associated purities. For multimode Gaussian states endowed
with local symmetry with respect to a given bipartition, we show how the
multimode block entanglement can be completely and reversibly localized onto a
single pair of modes by local, unitary operations. We then analyze the
distribution of entanglement among multiple parties in multimode Gaussian
states. We introduce the continuous-variable tangle to quantify entanglement
sharing in Gaussian states and we prove that it satisfies the
Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,
symmetric three-mode Gaussian states, at variance with their discrete-variable
counterparts, allow a promiscuous sharing of quantum correlations, exhibiting
both maximum tripartite residual entanglement and maximum couplewise
entanglement between any pair of modes. Finally, we investigate the connection
between multipartite entanglement and the optimal fidelity in a
continuous-variable quantum teleportation network. We show how the fidelity can
be maximized in terms of the best preparation of the shared entangled resources
and, viceversa, that this optimal fidelity provides a clearcut operational
interpretation of several measures of bipartite and multipartite entanglement,
including the entanglement of formation, the localizable entanglement, and the
continuous-variable tangle.Comment: 21 pages, 4 figures, WS style. Published as Chapter 1 in the book
"Quantum Information with Continuous Variables of Atoms and Light" (Imperial
College Press, 2007), edited by N. Cerf, G. Leuchs, and E. Polzik. Details of
the book available at http://www.icpress.co.uk/physics/p489.html . For recent
follow-ups see quant-ph/070122

### A Stochastic Approach to Thermal Fluctuations during a First Order Electroweak Phase Transition

We investigate the role played by subcritical bubbles at the onset of the
electroweak phase transition. Treating the configuration modelling the thermal
fluctuations around the homogeneous zero configuration of the Higgs field as a
stochastic variable, we describe its dynamics by a phenomenological Langevin
equation. This approach allows to properly take into account both the effects
of the thermal bath on the system: a systematic dyssipative force, which tends
to erase out any initial subcritical configuration, and a random stochastic
force responsible for the fluctuations. We show that the contribution to the
variance \lgh\phi^2(t)\rg_V in a given volume $V$ from any initial
subcritical configuration is quickly damped away and that, in the limit of long
times, \lgh\phi^2(t)\rg_V approaches its equilibrium value provided by the
stochastic force and independent from the viscosity coefficient, as predicted
by the fluctuation-dissipation theorem. In agreement with some recent claims,
we conclude that thermal fluctuations do not affect the nucleation of critical
bubbles at the onset of the electroweak phase transition making electroweak
baryogenesis scenarios still a viable possibility to explain the primordial
baryon asymmetry in the Universe.Comment: Two figures: fig1.metafile and fig2.metafile. Just print them as
usual file.p

### Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

We present a comprehensive analysis of the performance of different classes
of Gaussian states in the estimation of Gaussian phase-insensitive dissipative
channels. In particular, we investigate the optimal estimation of the damping
constant and reservoir temperature. We show that, for two-mode squeezed vacuum
probe states, the quantum-limited accuracy of both parameters can be achieved
simultaneously. Moreover, we show that for both parameters two-mode squeezed
vacuum states are more efficient than either coherent, thermal or single-mode
squeezed states. This suggests that at high energy regimes two-mode squeezed
vacuum states are optimal within the Gaussian setup. This optimality result
indicates a stronger form of compatibility for the estimation of the two
parameters. Indeed, not only the minimum variance can be achieved at fixed
probe states, but also the optimal state is common to both parameters.
Additionally, we explore numerically the performance of non-Gaussian states for
particular parameter values to find that maximally entangled states within
D-dimensional cutoff subspaces perform better than any randomly sampled states
with similar energy. However, we also find that states with very similar
performance and energy exist with much less entanglement than the maximally
entangled ones.Comment: 14 pages, 6 figure

### High-Temperature Atomic Superfluidity in Lattice Boson-Fermion Mixtures

We consider atomic Bose-Fermi mixtures in optical lattices and study the
superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion
interactions. We prove that the induced fermion-fermion coupling is always {\it
attractive} if the boson-boson on site interaction is repulsive, and predict
the existence of an enhanced BEC--BCS crossover as the strength of the lattice
potential is varied. We show that for direct on-site fermion-fermion {\it
repulsion}, the induced attraction can give rise to superfluidity via s-wave
pairing, at striking variance with the case of pure systems of fermionic atoms
with direct repulsive interactions.Comment: 4 pages, 2 figures, final versio

### Stochastic Variational Approach to Minimum Uncertainty States

We introduce a new variational characterization of Gaussian diffusion
processes as minimum uncertainty states. We then define a variational method
constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek
states of local minimum uncertainty for general non-harmonic potentials.Comment: 11 pages, latex, 12pt A4wide, no 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

### 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

### 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

### 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.

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