7,553 research outputs found
Moser-Trudinger inequality on conformal discs
We show that the Moser-Trudinger inequality holds in a conformal disc if and
only if the metric is bounded from above by the Hyperbolic metric. We also find
a necessary and sufficient condition for the Moser-Trudinger inequality to hold
in an unbounded subset of the two dimensional Euclidean space
Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice
in the presence of an external magnetic field by means of the equations of
motion method within the Green's function formalism. In particular, such an
approach is applied to an isomorphic model of localized Fermi particles
interacting via an intersite Coulomb interaction. A complete set of
eigenoperators is found together with the corresponding eigenvalues. The
Green's functions and the correlation functions are written in terms of a
finite set of parameters to be self-consistently determined. A procedure is
developed, that allows us to exactly fix the unknown parameters in the case of
a Bethe lattice with any coordination number z. Non-local correlation functions
up to four points are also provided together with a study of the relevant
thermodynamic quantities.Comment: RevTex, 29 pages, 13 figure
Determination of maximal Gaussian entanglement achievable by feedback-controlled dynamics
We determine a general upper bound for the steady-state entanglement
achievable by continuous feedback for systems of any number of bosonic degrees
of freedom. We apply such a bound to the specific case of parametric
interactions - the most common practical way to generate entanglement in
quantum optics - and single out optimal feedback strategies that achieve the
maximal entanglement. We also consider the case of feedback schemes entirely
restricted to local operations and compare their performance to the optimal,
generally nonlocal, schemes.Comment: 4 pages. Published versio
Reconstructing the density operator by using generalized field quadratures
The Wigner function for one and two-mode quantum systems is explicitely
expressed in terms of the marginal distribution for the generic linearly
transformed quadratures. Then, also the density operator of those systems is
written in terms of the marginal distribution of these quadratures. Some
examples to apply this formalism, and a reduction to the usual optical homodyne
tomography are considered.Comment: 17 pages, Latex,accepted by Quantum and Semiclassical Optic
Continuous quantum nondemolition feedback and unconditional atomic spin squeezing
We discuss the theory and experimental considerations of a quantum feedback
scheme for producing deterministically reproducible spin squeezing. Continuous
nondemolition atom number measurement from monitoring a probe field
conditionally squeezes the sample. Simultaneous feedback of the measurement
results controls the quantum state such that the squeezing becomes
unconditional. We find that for very strong cavity coupling and a limited
number of atoms, the theoretical squeezing approaches the Heisenberg limit.
Strong squeezing will still be produced at weaker coupling and even in free
space (thus presenting a simple experimental test for quantum feedback). The
measurement and feedback can be stopped at any time, thereby freezing the
sample with a desired amount of squeezing.Comment: 17 pages, 5 figures, submitted to JP
Transmitting qudits through larger quantum channels
We address the problem of transmitting states belonging to finite dimensional
Hilbert space through a quantum channel associated with a larger (even infinite
dimensional) Hilbert space.Comment: 5 pages, ReVTeX, minor changes, to appear in J. Phys.
Motional Squashed States
We show that by using a feedback loop it is possible to reduce the
fluctuations in one quadrature of the vibrational degree of freedom of a
trapped ion below the quantum limit. The stationary state is not a proper
squeezed state, but rather a ``squashed'' state, since the uncertainty in the
orthogonal quadrature, which is larger than the standard quantum limit, is
unaffected by the feedback action.Comment: 8 pages, 2 figures, to appear in the special Issue "Quantum
Correlations and Fluctuations" of J. Opt.
Quantum Characterization of a Werner-like Mixture
We introduce a Werner-like mixture [R. F. Werner, Phys. Rev. A {\bf 40}, 4277
(1989)] by considering two correlated but different degrees of freedom, one
with discrete variables and the other with continuous variables. We evaluate
the mixedness of this state, and its degree of entanglement establishing its
usefulness for quantum information processing like quantum teleportation. Then,
we provide its tomographic characterization. Finally, we show how such a
mixture can be generated and measured in a trapped system like one electron in
a Penning trap.Comment: 8 pages ReVTeX, 8 eps figure
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