Hierarchical and probabilistic quantum state sharing via a non-maximally entangled stateHierarchical and probabilistic quantum state sharing via a non-maximally entangled stateHierarchical and probabilistic quantum state sharing via a non-maximally entangled state

A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X） state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice＇s secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.     

关于 Fuzzyω正则语言的一个注记

通过引入ω-Nerode等价关系,fuzzy前逆缀ω-语言,闭左逆语言等概念来研究语言的化数性质,得到了(1)fuzzyω正则语言可由一些具有有限指标集的等价类来表示;(2)fuzzy前逆缀ω-语言是fuzzyω正则语言iff由L定义的ω-Nerode等价关系的指标集是有限的.     

Fuzzy正则表达式与Fuzzy有限态自动机的关系

首先给出了Fuzzy正则表达式的定义,接着通过研究Fuzzy正则表达式与Fuzzy有限态自动机的关系,得到了两个重要性质,即：每一个Fuzzy正则表达式,都有一个非确定性的Fuzzy有限态自动机接受其代表的语言;每一个被确定性的Fuzzy有限态自动机接受的语言,都能被一个Fuzzy正则表达式表示．     

Hierarchical and probabilistic quantum state sharing via a non-maximally entangled |χ〉 state

A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled |χ state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice’s secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.     

关于Fuzzy正则语言的一些性质

在定义Fuzzy正则语言,Fuzzy有理语言等的基础上,研究Fuzzy正则语言相关的一些性质,得到Fuzzy正则语言与Fuzzy有理语言间的对应关系,对Fuzzy有限状态自动机的简化具有应用价值。     

Fuzzyω正则语言的注记

定义P上的ω-Fuzzy等价关系的符号，并且定义了三上Fuzzy前缀逆相ω-语言和左逆封闭语言，在这些定义的基础上，得到了三上Fuzzy前缀逆相ω-语言是Fuzzy ω正则语言的充分必要条件是由L定义的ω-Fuzzy等价关系的指数有限，三上Fuzzy ω正则语言可以表示成∑^w上一些具有有限指数的左不变等价关系的某些等价类的并集。因而在由前缀逆相ω-语言或左逆封闭“语言组成的一语言类中，Fuzzy ω正则语言的代数特征就可从代数和集合论的观点给出。这为进一步研究Fuzzy有限状态自动机和Fuzzy正则语言奠定了基础。     

模糊Rabin自动机和模糊Game自动机的等价性

自动机是理论计算机的一个重要的研究内容.模糊Rabin自动机和模糊Game自动机是经典自动机的延续,给出了模糊Rabin自动机和模糊Game自动机的相关定义,讨论各自的内在性质,并得到了二者的等价关系.这进一步丰富了模糊自动机理论.     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

Joint Remote State Preparation of a Four-Dimensional Quantum State1

We present several protocols for joint remote state preparation of a single（two）-quadbit state with real （or complex） coefficients via a projective or positive operator-valued measure. In our schemes, three（five）-quadbit non-maximally entangled state（s） have been employed as the quantum channel and several appropriate mutually orthogonal basis are delicately constructed. Finally, the present schemes are extended to the （N ＋ M） senders＇ case.     

Fuzzy 上下文无关语言的Chomsky定理

在关于Fuzzy上下文无关语言的已有成果基础上,进一步考虑简化Fuzzy上下文无关文法,提出用派生刻画Fuzzy上下文无关文法与语言的性质,得到了Fuzzy上下文无关语言的Chomsky定理,并利用Pumping引理来判别一个语言是否为上下文无关语言.