116 research outputs found
Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?
We discuss the monotonicity under local operations and classical
communication (LOCC) of systematically constructed quantities aiming at
quantification of entanglement properties of multipartite quantum systems. The
so-called generalized multipartite concurrences can qualify as legitimate
entanglement measures if they are monotonous under LOCC. In the paper we give a
necessary and sufficient criterion for their monotonicity.Comment: 7 pages, 1 figure, minor changes - clarity of proofs improve
Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
The famous question of Mark Kac "Can one hear the shape of a drum?"
addressing the unique connection between the shape of a planar region and the
spectrum of the corresponding Laplace operator can be legitimately extended to
scattering systems. In the modified version one asks whether the geometry of a
vibrating system can be determined by scattering experiments. We present the
first experimental approach to this problem in the case of microwave graphs
(networks) simulating quantum graphs. Our experimental results strongly
indicate a negative answer. To demonstrate this we consider scattering from a
pair of isospectral microwave networks consisting of vertices connected by
microwave coaxial cables and extended to scattering systems by connecting leads
to infinity to form isoscattering networks. We show that the amplitudes and
phases of the determinants of the scattering matrices of such networks are the
same within the experimental uncertainties. Furthermore, we demonstrate that
the scattering matrices of the networks are conjugated by the, so called,
transplantation relation.Comment: 3 figures; Physical Review Letters, 201
Symplectic geometry of entanglement
We present a description of entanglement in composite quantum systems in
terms of symplectic geometry. We provide a symplectic characterization of sets
of equally entangled states as orbits of group actions in the space of states.
In particular, using Kostant-Sternberg theorem, we show that separable states
form a unique Kaehler orbit, whereas orbits of entanglement states are
characterized by different degrees of degeneracy of the canonical symplectic
form on the complex projective space. The degree of degeneracy may be thus used
as a new geometric measure of entanglement and we show how to calculate it for
various multiparticle systems providing also simple criteria of separability.
The presented method is general and can be applied also under different
additional symmetry conditions stemming, eg. from the indistinguishability of
particles.Comment: LaTex, 31 pages, typos correcte
Four-qubit entangled symmetric states with positive partial transpositions
We solve the open question of the existence of four-qubit entangled symmetric
states with positive partial transpositions (PPT states). We reach this goal
with two different approaches. First, we propose a
half-analytical-half-numerical method that allows to construct multipartite PPT
entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states.
Second, we adapt the algorithm allowing to search for extremal elements in the
convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum,
Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we
search for extremal four-qubit PPTESS and show that generically they have ranks
(5,7,8). Finally, we provide an exhaustive characterization of these states
with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie
Separable approximation for mixed states of composite quantum systems
We describe a purely algebraic method for finding the best separable
approximation to a mixed state of a composite 2x2 quantum system, consisting of
a decomposition of the state into a linear combination of a mixed separable
part and a pure entangled one. We prove that, in a generic case, the weight of
the pure part in the decomposition equals the concurrence of the state.Comment: 13 pages, no figures; minor changes; accepted for publication in PR
Barycentric measure of quantum entanglement
Majorana representation of quantum states by a constellation of n 'stars'
(points on the sphere) can be used to describe any pure state of a simple
system of dimension n+1 or a permutation symmetric pure state of a composite
system consisting of n qubits. We analyze the variance of the distribution of
the stars, which can serve as a measure of the degree of non-coherence for
simple systems, or an entanglement measure for composed systems. Dynamics of
the Majorana points induced by a unitary dynamics of the pure state is
investigated.Comment: 11 pages, 13 figure
Tunneling and the Band Structure of Chaotic Systems
We compute the dispersion laws of chaotic periodic systems using the
semiclassical periodic orbit theory to approximate the trace of the powers of
the evolution operator. Aside from the usual real trajectories, we also include
complex orbits. These turn out to be fundamental for a proper description of
the band structure since they incorporate conduction processes through
tunneling mechanisms. The results obtained, illustrated with the kicked-Harper
model, are in excellent agreement with numerical simulations, even in the
extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
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