314 research outputs found
The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.
Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,…
Entanglement in spin chains and lattices with long-range Ising-type interactions
We consider N initially disentangled spins, embedded in a ring or
d-dimensional lattice of arbitrary geometry, which interact via some
long--range Ising--type interaction. We investigate relations between
entanglement properties of the resulting states and the distance dependence of
the interaction in the limit N to infinity. We provide a sufficient condition
when bipartite entanglement between blocks of L neighboring spins and the
remaining system saturates, and determine S_L analytically for special
configurations. We find an unbounded increase of S_L as well as diverging
correlation and entanglement length under certain circumstances. For
arbitrarily large N, we can efficiently calculate all quantities associated
with reduced density operators of up to ten particles.Comment: 4 pages, 2 figures; V2: presentation improved, references adde
Nonergodicity of entanglement and its complementary behavior to magnetization in infinite spin chain
We consider the problem of the validity of a statistical mechanical
description of two-site entanglement in an infinite spin chain described by the
XY model Hamiltonian. We show that the two-site entanglement of the state,
evolved from the initial equilibrium state, after a change of the magnetic
field, does not approach its equilibrium value. This suggests that two-site
entanglement, like (single-site) magnetization, is a nonergodic quantity in
this model. Moreover we show that these two nonergodic quantities behave in a
complementary way.Comment: 4 pages, 2 eps figures, RevTeX4; v2: Published versio
The Influence of Structure Heights and Opening Angles of Micro- and Nanocones on the Macroscopic Surface Wetting Properties
We discuss the influence of surface structure, namely the height and opening angles of nano- and microcones on the surface wettability. We show experimental evidence that the opening angle of the cones is the critical parameter on sample superhydrophobicity, namely static contact angles and roll-off angles. The textured surfaces are fabricated on silicon wafers by using a simple one-step method of reactive ion etching at different processing time and gas flow rates. By using hydrophobic coating or hydrophilic surface treatment, we are able to switch the surface wettability from superhydrophilic to superhydrophobic without altering surface structures. In addition, we show examples of polymer replicas (polypropylene and poly(methyl methacrylate) with different wettability, fabricated by injection moulding using templates of the silicon cone-structures
Localizable Entanglement
We consider systems of interacting spins and study the entanglement that can
be localized, on average, between two separated spins by performing local
measurements on the remaining spins. This concept of Localizable Entanglement
(LE) leads naturally to notions like entanglement length and entanglement
fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a
pure quantum state can be lower bounded by connected correlation functions. We
further propose a scheme, based on matrix-product states and the Monte Carlo
method, to efficiently calculate the LE for quantum states of a large number of
spins. The virtues of LE are illustrated for various spin models. In
particular, characteristic features of a quantum phase transition such as a
diverging entanglement length can be observed. We also give examples for pure
quantum states exhibiting a diverging entanglement length but finite
correlation length. We have numerical evidence that the ground state of the
antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum
channel. Furthermore, we apply the numerical method to mixed states and study
the entanglement as a function of temperature.Comment: 19 pages, modified definition of connected string order parameter,
updated reference
Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing
We consider the problem of deciding if a given three-party entangled pure
state can be converted, with a non-zero success probability, into a given
two-party pure state through local quantum operations and classical
communication. We show that this question is equivalent to the well-known
computational problem of deciding if a multivariate polynomial is identically
zero. Efficient randomized algorithms developed to study the latter can thus be
applied to the question of tripartite to bipartite entanglement
transformations
Maximizing nearest neighbour entanglement in finitely correlated qubit--chains
We consider translationally invariant states of an infinite one dimensional
chain of qubits or spin-1/2 particles. We maximize the entanglement shared by
nearest neighbours via a variational approach based on finitely correlated
states. We find an upper bound of nearest neighbour concurrence equal to
C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a
completely different procedure. The obtained state maximizing nearest neighbour
entanglement seems to approximate the maximally entangled mixed states (MEMS).
Further we investigate in detail several other properties of the so obtained
optimal state.Comment: 12 pages, 4 figures, 2nd version minor change
Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
We search for translationally invariant states of qubits on a ring that
maximize the nearest neighbor entanglement. This problem was initially studied
by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map
the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ
model. Using the exact Bethe ansatz solution in the limit of an infinite ring,
we prove the correctness of the assumption of O'Connor and Wootters that the
state of maximal entanglement does not have any pair of neighboring spins
``down'' (or, alternatively spins ``up''). For sufficiently small fixed
magnetization, however, the assumption does not hold: we identify the region of
magnetizations for which the states that maximize the nearest neighbor
entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative
change in conclusion
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