659 research outputs found
Classification of mixed three-qubit states
We introduce a classification of mixed three-qubit states, in which we define
the classes of separable, biseparable, W- and GHZ-states. These classes are
successively embedded into each other. We show that contrary to pure W-type
states, the mixed W-class is not of measure zero. We construct witness
operators that detect the class of a mixed state. We discuss the conjecture
that all entangled states with positive partial transpose (PPTES) belong to the
W-class. Finally, we present a new family of PPTES "edge" states with maximal
ranks.Comment: 4 pages, 1 figur
Entanglement Distillation Protocols and Number Theory
We show that the analysis of entanglement distillation protocols for qudits
of arbitrary dimension benefits from applying basic concepts from number
theory, since the set \zdn associated to Bell diagonal states is a module
rather than a vector space. We find that a partition of \zdn into divisor
classes characterizes the invariant properties of mixed Bell diagonal states
under local permutations. We construct a very general class of recursion
protocols by means of unitary operations implementing these local permutations.
We study these distillation protocols depending on whether we use twirling
operations in the intermediate steps or not, and we study them both
analitically and numerically with Monte Carlo methods. In the absence of
twirling operations, we construct extensions of the quantum privacy algorithms
valid for secure communications with qudits of any dimension . When is a
prime number, we show that distillation protocols are optimal both
qualitatively and quantitatively.Comment: REVTEX4 file, 7 color figures, 2 table
Generalized spin squeezing inequalities in qubit systems: theory and experiment
We present detailed derivations, various improvements and application to
concrete experimental data of spin squeezing inequalities formulated recently
by some of us [Phys. Rev. Lett. {\bf 95}, 120502 (2005)]. These inequalities
generalize the concept of the spin squeezing parameter, and provide necessary
and sufficient conditions for genuine 2-, or 3- qubit entanglement for
symmetric states, and sufficient entanglement condition for general -qubit
states. We apply our method to theoretical study of Dicke states, and, in
particular, to -states of qubits. Then, we analyze the recently
experimentally generated 7- and 8-ion -states [Nature {\bf 438}, 643
(2005)]. We also present some novel details concerning this experiment.
Finally, we improve criteria for detection of genuine tripartite entanglement
based on entanglement witnesses.Comment: Final versio
Separable approximations of density matrices of composite quantum systems
We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure
Cooperative quantum jumps for three dipole-interacting atoms
We investigate the effect of the dipole-dipole interaction on the quantum
jump statistics of three atoms. This is done for three-level systems in a V
configuration and in what may be called a D configuration. The transition rates
between the four different intensity periods are calculated in closed form.
Cooperative effects are shown to increase by a factor of 2 compared to two of
either three-level systems. This results in transition rates that are, for
distances of about one wavelength of the strong transition, up to 100% higher
than for independent systems. In addition the double and triple jump rates are
calculated from the transition rates. In this case cooperative effects of up to
170% for distances of about one wavelength and still up to 15% around 10
wavelengths are found. Nevertheless, for the parameters of an experiment with
Hg+ ions the effects are negligible, in agreement with the experimental data.
For three Ba+ ions this seems to indicate that the large cooperative effects
observed experimentally cannot be explained by the dipole-dipole interaction.Comment: 9 pages, 9 figures. Revised version, to be published in PR
Atomic quantum gases in Kagom\'e lattices
We demonstrate the possibility of creating and controlling an ideal and
\textit{trimerized} optical Kagom\'e lattice, and study the low temperature
physics of various atomic gases in such lattices. In the trimerized Kagom\'e
lattice, a Bose gas exhibits a Mott transition with fractional filling factors,
whereas a spinless interacting Fermi gas at 2/3 filling behaves as a quantum
magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half filling
for both components represents a frustrated quantum antiferromagnet with a
resonating-valence-bond ground state and quantum spin liquid behavior dominated
by continuous spectrum of singlet and triplet excitations. We discuss the
method of preparing and observing such quantum spin liquid employing molecular
Bose condensates.Comment: 4 pages, 1 figure. Missing affiliations adde
High-order harmonic generation from inhomogeneous fields
We present theoretical studies of high-order harmonic generation (HHG)
produced by non-homogeneous fields as resulting from the illumination of
plasmonic nanostructures with a short laser pulse. We show that both the
inhomogeneity of the local fields and the confinement of the electron movement
play an important role in the HHG process and lead to the generation of even
harmonics and a significantly increased cutoff, more pronounced for the longer
wavelengths cases studied. In order to understand and characterize the new HHG
features we employ two different approaches: the numerical solution of the time
dependent Schr\"odinger equation (TDSE) and the semiclassical approach known as
Strong Field Approximation (SFA). Both approaches predict comparable results
and show the new features, but using the semiclassical arguments behind the SFA
and time-frequency analysis tools, we are able to fully understand the reasons
of the cutoff extension.Comment: 25 pages, 12 figure
Sympathetic cooling of trapped fermions by bosons in the presence of particle losses
We study the sympathetic cooling of a trapped Fermi gas interacting with an
ideal Bose gas below the critical temperature of the Bose-Einstein
condensation. We derive the quantum master equation, which describes the
dynamics of the fermionic component, and postulating the thermal distribution
for both gases we calculate analytically the rate at which fermions are cooled
by the bosonic atoms. The particle losses constitute an important source of
heating of the degenerate Fermi gas. We evaluate the rate of loss-induced
heating and derive analytical results for the final temperature of fermions,
which is limited in the presence of particle losses.Comment: 7 pages, 2 figures, EPL style; final versio
Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
We study entanglement in mixed bipartite quantum states which are invariant
under simultaneous SU(2) transformations in both subsystems. Previous results
on the behavior of such states under partial transposition are substantially
extended. The spectrum of the partial transpose of a given SU(2)-invariant
density matrix is entirely determined by the diagonal elements of
in a basis of tensor-product states of both spins with respect to a common
quantization axis. We construct a set of operators which act as entanglement
witnesses on SU(2)-invariant states. A sufficient criterion for having a
negative partial transpose is derived in terms of a simple spin correlator. The
same condition is a necessary criterion for the partial transpose to have the
maximum number of negative eigenvalues. Moreover, we derive a series of sum
rules which uniquely determine the eigenvalues of the partial transpose in
terms of a system of linear equations. Finally we compare our findings with
other entanglement criteria including the reduction criterion, the majorization
criterion, and the recently proposed local uncertainty relations.Comment: 7 pages, no figures, version to appear in Phys. Rev.
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