1,345 research outputs found
All Maximally Entangled Four Qubits States
We find an operational interpretation for the 4-tangle as a type of residual
entanglement, somewhat similar to the interpretation of the 3-tangle. Using
this remarkable interpretation, we are able to find the class of maximally
entangled four-qubits states which is characterized by four real parameters.
The states in the class are maximally entangled in the sense that their average
bipartite entanglement with respect to all possible bi-partite cuts is maximal.
We show that while all the states in the class maximize the average tangle,
there are only few states in the class that maximize the average Tsillas or
Renyi -entropy of entanglement. Quite remarkably, we find that up to
local unitaries, there exists two unique states, one maximizing the average
-Tsallis entropy of entanglement for all , while the
other maximizing it for all (including the von-Neumann case of
). Furthermore, among the maximally entangled four qubits states,
there are only 3 maximally entangled states that have the property that for 2,
out of the 3 bipartite cuts consisting of 2-qubits verses 2-qubits, the
entanglement is 2 ebits and for the remaining bipartite cut the entanglement
between the two groups of two qubits is 1ebit. The unique 3 maximally entangled
states are the 3 cluster states that are related by a swap operator. We also
show that the cluster states are the only states (up to local unitaries) that
maximize the average -Renyi entropy of entanglement for all .Comment: 15 pages, 2 figures, Revised Version: many references added, an
appendix added with a statement of the Kempf-Ness theore
Optimal decomposable witnesses without the spanning property
One of the unsolved problems in the characterization of the optimal
entanglement witnesses is the existence of optimal witnesses acting on
bipartite Hilbert spaces H_{m,n}=C^m\otimes C^n such that the product vectors
obeying =0 do not span H_{m,n}. So far, the only known examples of
such witnesses were found among indecomposable witnesses, one of them being the
witness corresponding to the Choi map. However, it remains an open question
whether decomposable witnesses exist without the property of spanning. Here we
answer this question affirmatively, providing systematic examples of such
witnesses. Then, we generalize some of the recently obtained results on the
characterization of 2\otimes n optimal decomposable witnesses [R. Augusiak et
al., J. Phys. A 44, 212001 (2011)] to finite-dimensional Hilbert spaces H_{m,n}
with m,n\geq 3.Comment: 11 pages, published version, title modified, some references added,
other minor improvement
Entanglement of subspaces in terms of entanglement of superpositions
We investigate upper and lower bounds on the entropy of entanglement of a
superposition of bipartite states as a function of the individual states in the
superposition. In particular, we extend the results in [G. Gour,
arxiv.org:0704.1521 (2007)] to superpositions of several states rather than
just two. We then investigate the entanglement in a subspace as a function of
its basis states: we find upper bounds for the largest entanglement in a
subspace and demonstrate that no such lower bound for the smallest entanglement
exists. Finally, we consider entanglement of superpositions using measures of
entanglement other than the entropy of entanglement.Comment: 7 pages, no figure
Classification of unitary highest weight representations for non compact real forms
Using Jakobsen theorems, unitarizability in Hermitian Symmetric Spaces is
discussed. The set of all missing highest weights is explicitly calculated and
the construction of their corresponding highest weights vectors is studied.Comment: PDF, 35 pages (late submission
A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces
Entanglement witnesses (EWs) constitute one of the most important
entanglement detectors in quantum systems. Nevertheless, their complete
characterization, in particular with respect to the notion of optimality, is
still missing, even in the decomposable case. Here we show that for any
qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i)
the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the
corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^{\Gamma} with Q
denoting a positive operator supported on a completely entangled subspace (CES)
and \Gamma standing for the partial transposition. While, implications
and are known, here we prove that
(iii) implies (i). This is a consequence of a more general fact saying that
product vectors orthogonal to any CES in C^{2}\otimes C^{n} span after partial
conjugation the whole space. On the other hand, already in the case of
C^{3}\otimes C^{3} Hilbert space, there exist DEWs for which (iii) does not
imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply
(iii), and the above transparent characterization obeyed by qubit-qunit DEWs,
does not hold in general.Comment: 13 pages, proof of lemma 4 corrected, theorem 3 removed, some parts
improve
On the dimension of subspaces with bounded Schmidt rank
We consider the question of how large a subspace of a given bipartite quantum
system can be when the subspace contains only highly entangled states. This is
motivated in part by results of Hayden et al., which show that in large d x
d--dimensional systems there exist random subspaces of dimension almost d^2,
all of whose states have entropy of entanglement at least log d - O(1). It is
also related to results due to Parthasarathy on the dimension of completely
entangled subspaces, which have connections with the construction of
unextendible product bases. Here we take as entanglement measure the Schmidt
rank, and determine, for every pair of local dimensions dA and dB, and every r,
the largest dimension of a subspace consisting only of entangled states of
Schmidt rank r or larger. This exact answer is a significant improvement on the
best bounds that can be obtained using random subspace techniques. We also
determine the converse: the largest dimension of a subspace with an upper bound
on the Schmidt rank. Finally, we discuss the question of subspaces containing
only states with Schmidt equal to r.Comment: 4 pages, REVTeX4 forma
Unitary derived functor modules with small spectrum
This article does not have an abstract
Maternal transfer of antibodies induced by infection with Eimeria maxima partially protects chickens against challenge with Eimeria tenella
Infection of breeding hens with Eimeria maxima induces production of Eimeria-specific IgG antibodies which are transferred to hatchlings via the egg yolk and confer a high degree of maternal immunity against homologous challenge and partial immunity to infection with another important species, Eimeria tenella. As an example, in an experiment using hatchlings from eggs collected between days 28 and 39 after infection of the hens with 20 000 sporulated E. maxima oocysts, control chicks (challenged with 100 sporulated oocysts) excreted 6·8±1·2 million (mean±s.e., n = 10) or 5·8±1·2 million (n = 8) oocysts of E. maxima or E. tenella, respectively, compared to 0·9±0·4 million (n = 5) E. maxima oocysts or 2·2±0·4 million (n = 9) E. tenella oocysts excreted by hatchlings of infected hens. This represents an 87% reduction in oocyst excretion with regard to E. maxima and a 62% reduction in oocyst excretion with regard to E. tenella in the progeny of the infected hens. In another experiment, eggs were collected from days 28 to 37 and again from days 114 to 123 after infection of the hens with E. maxima and hatchling oocyst excretion rates were 82% and 62%, respectively, reduced for E. maxima and 43% and 41%, respectively, reduced for E. tenella in the progeny of hens infected with E. maxima compared to the progeny of uninfected hens. ELISA and Western blot analyses of maternally-derived IgG revealed a high degree of cross-reactivity to antigens of E. maxima and E. tenella. Thus, maternally-derived, IgG-mediated cross- resistance to different species of Eimeria occurs in the chicken, most likely as a result of cross-recognition of conserved epitopes or protein
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