885 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
A variant of multitask n-vehicle exploration problem: maximizing every processor's average profit
We discuss a variant of multitask n-vehicle exploration problem. Instead of
requiring an optimal permutation of vehicles in every group, the new problem
asks all vehicles in a group to arrive at a same destination. It can also be
viewed as to maximize every processor's average profit, given n tasks, and each
task's consume-time and profit. Meanwhile, we propose a new kind of partition
problem in fractional form, and analyze its computational complexity. Moreover,
by regarding fractional partition as a special case, we prove that the
maximizing average profit problem is NP-hard when the number of processors is
fixed and it is strongly NP-hard in general. At last, a pseudo-polynomial time
algorithm for the maximizing average profit problem and the fractional
partition problem is presented, thanks to the idea of the pseudo-polynomial
time algorithm for the classical partition problem.Comment: This work is part of what I did as a graduate student in the Academy
of Mathematics and Systems Scienc
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
Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems
The error bound property for a solution set defined by a set-valued mapping
refers to an inequality that bounds the distance between vectors closed to a
solution of the given set by a residual function. The error bound property is a
Lipschitz-like/calmness property of the perturbed solution mapping, or
equivalently the metric subregularity of the underlining set-valued mapping. It
has been proved to be extremely useful in analyzing the convergence of many
algorithms for solving optimization problems, as well as serving as a
constraint qualification for optimality conditions. In this paper, we study the
error bound property for the solution set of a very general second-order cone
complementarity problem (SOCCP). We derive some sufficient conditions for error
bounds for SOCCP which is verifiable based on the initial problem data
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
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