Nonlinear Jordan Higher Derivations of Triangular Algebras

In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb...     

Geometry of skew information-based quantum coherence

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases (MUBs). We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs. Moreover, we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels. The results show similar as well as different features compared with relative entropy of coherence and l₁ norm of coherence.     

Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.     

算子代数上2-局部Lie三重导子的结构

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和.