102 research outputs found
Uncertainty relations for any multi observables
Uncertainty relations describe the lower bound of product of standard
deviations of observables. By revealing a connection between standard
deviations of quantum observables and numerical radius of operators, we
establish a universal uncertainty relation for any observables, of which
the formulation depends on the even or odd quality of . This universal
uncertainty relation is tight at least for the cases and . For two
observables, the uncertainty relation is exactly a simpler reformulation of
Schr\"odinger's uncertainty principle.Comment: 16 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
Strong -commutativity preserving maps on 22 matrices
Let be the algebra of 22 matrices over
the real or complex field . For a given positive integer ,
the -commutator of and is defined by with
and . The main result is shown that a map
with range
containing all rank one matrices satisfies that for all if and only if there exist a
functional and a scalar
with such that for all .Comment: 12 page
Strong -Commutativity Preserving Maps on Standard Operator Algebras
Let be a Banach space of dimension over the real or complex
field and
a standard operator algebra in . A map
is said to be strong
-commutativity preserving if for all , where is the 3-commutator of defined by
. The main result in this paper is shown that, if
is a surjective map on , then is strong -commutativity
preserving if and only if there exist a functional and a scalar with such
that for all .Comment: 14 page
Criteria of positivity for linear maps constructed from permutation pairs
In this paper, we show that a -type map with
induced by a pair
of permutations of is positive if
has property (C). The property (C) is characterized for
, and an easy criterion is given for the case that
and , where is the permutation defined by
mod and
Non-linear maps on self-adjoint operators preserving numerical radius and numerical range of Lie product
Let be a complex separable Hilbert space of dimension ,
the space of all self-adjoint operators on . We give a
complete classification of non-linear surjective maps on
preserving respectively numerical radius and numerical range of Lie product.Comment: 22 page
Entanglement criterion independent on observables for multipartite Gaussian states based on uncertainty principle
The local uncertainty relation (LUR) criteria for quantum entanglement, which
is dependent on chosen observables, is developed recent. In the paper, applying
the uncertainty principle, an entanglement criteria for multipartite Gaussian
states is given, which is implemented by a minimum optimization computer
program and independent on observalbes.Comment: 9 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
The RCCN criterion of separability for states in infinite-dimensional quantum systems
In this paper, the realignment criterion and the RCCN criterion of
separability for states in infinite-dimensional bipartite quantum systems are
established. Let and be complex Hilbert spaces with . Let be a state on and
be the Schmidt coefficients of as a vector in the Hilbert
space . We introduce the
realignment operation and the computable cross norm of and show that, if is separable, then In particular, if is
a pure state, then is separable if and only if .Comment: 18 page
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
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