429 research outputs found
Strong skew commutativity preserving maps on von Neumann algebras
Let be a von Neumann algebra without central summands of type
. Assume that is a surjective
map. It is shown that is strong skew commutativity preserving (that is,
satisfies for all ) if and only if there exists some self-adjoint element in the center of
with such that for all .
The strong skew commutativity preserving maps on prime involution rings and
prime involution algebras are also characterized.Comment: 16 page
Detecting entanglement of states by entries of their density matrices
For any bipartite systems, a universal entanglement witness of rank-4 for
pure states is obtained and a class of finite rank entanglement witnesses is
constructed. In addition, a method of detecting entanglement of a state only by
entries of its density matrix with respect to some product basis is obtained.Comment: 14 page
A characterization of optimal entanglement witnesses
In this paper, we present a characterization of optimal entanglement
witnesses in terms of positive maps and then provide a general method of
checking optimality of entanglement witnesses. Applying it, we obtain new
indecomposable optimal witnesses which have no spanning property. These also
provide new examples which support a recent conjecture saying that the
so-called structural physical approximations to optimal positive maps (optimal
entanglement witnesses) give entanglement breaking maps (separable states).Comment: 1
Positive finite rank elementary operators and characterizing entanglement of states
In this paper, a class of indecomposable positive finite rank elementary
operators of order are constructed. This allows us to give a simple
necessary and sufficient criterion for separability of pure states in bipartite
systems of any dimension in terms of positive elementary operators of order
and get some new mixed entangled states that can not be detected by the
positive partial transpose (PPT) criterion and the realignment criterion.Comment: 26 page
Linear maps preserving separability of pure states
Linear maps preserving pure states of a quantum system of any dimension are
characterized. This is then used to establish a structure theorem for linear
maps that preserve separable pure states in multipartite systems. As an
application, a characterization of separable pure state preserving affine maps
is obtained.Comment: 16 page
Fidelity of states in infinite dimensional quantum systems
In this paper we discuss the fidelity of states in infinite dimensional
systems, give an elementary proof of the infinite dimensional version of
Uhlmann's theorem, and then, apply it to generalize several properties of the
fidelity from finite dimensional case to infinite dimensional case. Some of
them are somewhat different from those for finite dimensional case.Comment: 12 page
Optimality of a class of entanglement witnesses for systems
Let be a linear
map defined by
,
where and is a permutation of . We show that the
Hermitian matrix induced by is an optimal
entanglement witness if and only if and is cyclic.Comment: 12 page
Coherence measures and optimal conversion for coherent states
We discuss a general strategy to construct coherence measures. One can build
an important class of coherence measures which cover the relative entropy
measure for pure states, the -norm measure for pure states and the
-entropy measure. The optimal conversion of coherent states under
incoherent operations is presented which sheds some light on the coherence of a
single copy of a pure state.Comment: in Quantum Information & Computation 201
Lie ring isomorphisms between nest algebras on Banach spaces
Let and be nests on Banach spaces and
over the (real or complex) field and let \mbox{\rm Alg}{\mathcal
N} and \mbox{\rm Alg}{\mathcal M} be the associated nest algebras,
respectively. It is shown that a map is a Lie ring isomorphism (i.e., is additive, Lie
multiplicative and bijective) if and only if has the form for all A\in \mbox{\rm Alg}{\mathcal N} or
for all A\in \mbox{\rm Alg}{\mathcal N}, where
is an additive functional vanishing on all commutators and is an
invertible bounded linear or conjugate linear operator when ;
is a bijective -linear transformation for some field automorphism
of when .Comment: 27 page
Characterizing derivations for any nest algebras on Banach spaces by their behaviors at an injective operator
Let be a nest on a complex Banach space and let \mbox{
Alg}{\mathcal N} be the associated nest algebra. We say that an operator Z\in
\mbox{ Alg}{\mathcal N} is an all-derivable point of \mbox{ Alg}{\mathcal N}
if every linear map from \mbox{ Alg}{\mathcal N} into itself
derivable at (i.e. satisfies for
any A,B \in \mbox{ Alg}{\mathcal N} with ) is a derivation. In this
paper, it is shown that every injective operator and every operator with dense
range in \mbox{Alg}{\mathcal N} are all-derivable points of
\mbox{Alg}{\mathcal N} without any additional assumption on the nest.Comment: 20 page
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