1,768 research outputs found
Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs
The structure of all completely positive quantum operations is investigated
which transform pure two-qubit input states of a given degree of entanglement
in a covariant way. Special cases thereof are quantum NOT operations which
transform entangled pure two-qubit input states of a given degree of
entanglement into orthogonal states in an optimal way. Based on our general
analysis all covariant optimal two-qubit quantum NOT operations are determined.
In particular, it is demonstrated that only in the case of maximally entangled
input states these quantum NOT operations can be performed perfectly.Comment: 14 pages, 2 figure
Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
The algebraic-geometric approach is extended to study solutions of
N-component systems associated with the energy dependent Schrodinger operators
having potentials with poles in the spectral parameter, in connection with
Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems
under study include the shallow water equation and Dym type equation. The
classes of solutions are described in terms of theta-functions and their
singular limits by using new parameterizations. A qualitative description of
real valued solutions is provided
Class of PPT bound entangled states associated to almost any set of pure entangled states
We analyze a class of entangled states for bipartite systems,
with non-prime. The entanglement of such states is revealed by the
construction of canonically associated entanglement witnesses. The structure of
the states is very simple and similar to the one of isotropic states: they are
a mixture of a separable and a pure entangled state whose supports are
orthogonal. Despite such simple structure, in an opportune interval of the
mixing parameter their entanglement is not revealed by partial transposition
nor by the realignment criterion, i.e. by any permutational criterion in the
bipartite setting. In the range in which the states are Positive under Partial
Transposition (PPT), they are not distillable; on the other hand, the states in
the considered class are provably distillable as soon as they are Nonpositive
under Partial Transposition (NPT). The states are associated to any set of more
than two pure states. The analysis is extended to the multipartite setting. By
an opportune selection of the set of multipartite pure states, it is possible
to construct mixed states which are PPT with respect to any choice of bipartite
cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we
show that every -positive but not completely positive map is associated to a
family of nondecomposable maps.Comment: 12 pages, 3 figures. To appear in Phys. Rev.
Continuous macroscopic limit of a discrete stochastic model for interaction of living cells
In the development of multiscale biological models it is crucial to establish
a connection between discrete microscopic or mesoscopic stochastic models and
macroscopic continuous descriptions based on cellular density. In this paper a
continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded
volume is derived, describing cells moving in a medium and reacting to each
other through both direct contact and long range chemotaxis. The continuous
macroscopic model is obtained as a Fokker-Planck equation describing evolution
of the cell probability density function. All coefficients of the general
macroscopic model are derived from parameters of the CPM and a very good
agreement is demonstrated between CPM Monte Carlo simulations and numerical
solution of the macroscopic model. It is also shown that in the absence of
contact cell-cell interactions, the obtained model reduces to the classical
macroscopic Keller-Segel model. General multiscale approach is demonstrated by
simulating spongy bone formation from loosely packed mesenchyme via the
intramembranous route suggesting that self-organizing physical mechanisms can
account for this developmental process.Comment: 4 pages, 3 figure
Entanglement quantification through local observable correlations
We present a significantly improved scheme of entanglement detection inspired
by local uncertainty relations for a system consisting of two qubits.
Developing the underlying idea of local uncertainty relations, namely
correlations, we demonstrate that it's possible to define a measure which is
invariant under local unitary transformations and which is based only on local
measurements. It is quite simple to implement experimentally and it allows
entanglement quantification in a certain range for mixed states and exactly for
pure states, without first obtaining full knowledge (e.g. through tomography)
of the state.Comment: 5 pages, 3 figures, revised version with new proof and replaced
figure
Thermal entanglement witness for materials with variable local spin lengths
We show that the thermal entanglement in a spin system using only magnetic
susceptibility measurements is restricted to the insulator materials. We
develop a generalization of the thermal entanglement witness that allows us to
get information about the system entanglement with variable local spin lengths
that can be used experimentally in conductor or insulator materials. As an
application, we study thermal entanglement for the half-filled Hubbard model
for linear, square and cubic clusters. We note that it is the itinerancy of
electrons that favors the entanglement. Our results suggest a weak dependence
between entanglement and external spin freedom degrees.Comment: 4 pages, 3 figure
Optimal copying of entangled two-qubit states
We investigate the problem of copying pure two-qubit states of a given degree
of entanglement in an optimal way. Completely positive covariant quantum
operations are constructed which maximize the fidelity of the output states
with respect to two separable copies. These optimal copying processes hint at
the intricate relationship between fundamental laws of quantum theory and
entanglement.Comment: 13 pages, 7 figure
Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime
We explore possibilities of entangling two distant material qubits with the
help of an optical radiation field in the regime of strong quantum
electrodynamical coupling with almost resonant interaction. For this purpose
the optimum generalized field measurements are determined which are capable of
preparing a two-qubit Bell state by postselection with minimum error. It is
demonstrated that in the strong-coupling regime some of the recently found
limitations of the non-resonant weak-coupling regime can be circumvented
successfully due to characteristic quantum electrodynamical quantum
interference effects. In particular, in the absence of photon loss it is
possible to postselect two-qubit Bell states with fidelities close to unity by
a proper choice of the relevant interaction time. Even in the presence of
photon loss this strong-coupling regime offers interesting perspectives for
creating spatially well-separated Bell pairs with high fidelities, high success
probabilities, and high repetition rates which are relevant for future
realizations of quantum repeaters.Comment: 14 pages, 12 figure
- …