70 research outputs found
Correlation constraints and the Bloch geometry of two qubits
We present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we construct a three-dimensional Bloch model of the two-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations
Generalized W-Class State and its Monogamy Relation
We generalize the W class of states from qubits to qudits and prove
that their entanglement is fully characterized by their partial entanglements
even for the case of the mixture that consists of a W-class state and a product
state .Comment: 12 pages, 1 figur
Rescaling multipartite entanglement measures for mixed states
A relevant problem regarding entanglement measures is the following: Given an
arbitrary mixed state, how does a measure for multipartite entanglement change
if general local operations are applied to the state? This question is
nontrivial as the normalization of the states has to be taken into account.
Here we answer it for pure-state entanglement measures which are invariant
under determinant 1 local operations and homogeneous in the state coefficients,
and their convex-roof extension which quantifies mixed-state entanglement. Our
analysis allows to enlarge the set of mixed states for which these important
measures can be calculated exactly. In particular, our results hint at a
distinguished role of entanglement measures which have homogeneous degree 2 in
the state coefficients.Comment: Published version plus one important reference (Ref. [39]
Three-tangle for mixtures of generalized GHZ and generalized W states
We give a complete solution for the three-tangle of mixed three-qubit states
composed of a generalized GHZ state, a|000>+b|111>, and a generalized W state,
c|001>+d|010>+f|100>. Using the methods introduced by Lohmayer et al. we
provide explicit expressions for the mixed-state three-tangle and the
corresponding optimal decompositions for this more general case. Moreover, as a
special case we obtain a general solution for a family of states consisting of
a generalized GHZ state and an orthogonal product state
Correlation between magnetic spin structure and the three-dimensional geometry in chemically synthesized nanoscale magnetite rings
The correlation between magnetic spin structure and geometry in nanoscale chemically synthesized Fe(3)O(4) rings has been investigated by transmission electron microscopy. We find primarily the flux closure vortex states but in rings with thickness variations, an effective stray field occurs. Using tomography, we determine the complete three-dimensional geometries of thicker rings. A direct correlation between the geometry and the magnetization which points out of plane in the thickest parts of the ring yielding an intermediate magnetic state between the vortex state and the tube state is found. The interaction between exchange coupled rings leads to antiparallel vortex states and extended onion states. (c) 2008 American Institute of Physics.Physics, AppliedSCI(E)EI2ARTICLE22null9
Classification of qubit entanglement: SL(2,C) versus SU(2) invariance
The role of SU(2) invariants for the classification of multiparty
entanglement is discussed and exemplified for the Kempe invariant I_5 of pure
three-qubit states. It is found to being an independent invariant only in
presence of both W-type entanglement and threetangle. In this case, constant
I_5 admits for a wide range of both threetangle and concurrences. Furthermore,
the present analysis indicates that an SL^3 orbit of states with equal tangles
but continuously varying I_5 must exist. This means that I_5 provides no
information on the entanglement in the system in addition to that contained in
the tangles (concurrences and threetangle) themselves. Together with the
numerical evidence that I_5 is an entanglement monotone this implies that SU(2)
invariance or the monotone property are too weak requirements for the
characterization and quantification of entanglement for systems of three
qubits, and that SL(2,C) invariance is required. This conclusion can be
extended to general multipartite systems (including higher local dimension)
because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex
Measurements in two bases are sufficient for certifying high-dimensional entanglement
High-dimensional encoding of quantum information provides a promising method
of transcending current limitations in quantum communication. One of the
central challenges in the pursuit of such an approach is the certification of
high-dimensional entanglement. In particular, it is desirable to do so without
resorting to inefficient full state tomography. Here, we show how carefully
constructed measurements in two bases (one of which is not orthonormal) can be
used to faithfully and efficiently certify bipartite high-dimensional states
and their entanglement for any physical platform. To showcase the practicality
of this approach under realistic conditions, we put it to the test for photons
entangled in their orbital angular momentum. In our experimental setup, we are
able to verify 9-dimensional entanglement for a pair of photons on a
11-dimensional subspace each, at present the highest amount certified without
any assumptions on the state.Comment: 11+14 pages, 2+7 figure
Resonance- and Chaos-Assisted Tunneling
We consider dynamical tunneling between two symmetry-related regular islands
that are separated in phase space by a chaotic sea. Such tunneling processes
are dominantly governed by nonlinear resonances, which induce a coupling
mechanism between ``regular'' quantum states within and ``chaotic'' states
outside the islands. By means of a random matrix ansatz for the chaotic part of
the Hamiltonian, one can show that the corresponding coupling matrix element
directly determines the level splitting between the symmetric and the
antisymmetric eigenstates of the pair of islands. We show in detail how this
matrix element can be expressed in terms of elementary classical quantities
that are associated with the resonance. The validity of this theory is
demonstrated with the kicked Harper model.Comment: 25 pages, 5 figure
A quantitative witness for Greenberger-Horne-Zeilinger entanglement
Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger–type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties
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