Analysis of a tripartite entanglement distribution switch

Queueing Systems - We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to...     

Separability and distance

Translated from Matematicheskie Zametki, Vol. 50, No. 5, pp. 18–22, November, 1991.     

Separability and triangulated categories

We prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one. This applies in particular to étale algebras. More generally, we do this for exact separable monads.     

On Sequential Separability

A new criterion for the sequential separability of the space C(X) of continuous real-valued functions on X in the topology of simple convergence is obtained.     

Effect of atomic decay on purity,total correlations and entanglement of pure and mixed states

The atomic decay for a two level atom interacting with a single mode of electromagnetic field is considered. In particular for a coherent state or statistical mixture (SM) of two opposite coherent states as initial field states, the exact solution of the master equation is found. Effect of the atomic damping on the partial entropies of the atom or the field and the total entropy as a measures of the purity loss is investigated. The degree of entanglement by the negativity and the mutual information and the atomic coherence through the master equation is studied.     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

Separability and the Twisted Frobenius Bimodule

This paper begins with an introduction to -Frobenius structure on a finite-dimensional Hopf subalgebra pair. In Section 2 a study is made of a generalization of Frobenius bimodules and -Frobenius extensions. Also a special type of twisted Frobenius bimodule which gives an endomorphism ring theorem and converse is studied. Section 3 brings together material on separable bimodules, the dual definitions of split and separable extension, and a theorem of Sugano on endomorphism rings of separable bimodules. In Section 4, separable twisted Frobenius bimodules are characterized in terms of data that generalizes a Frobenius homomorphism and a dual base. In the style of duality, two corollaries characterizing split -Frobenius and separable -Frobenius extensions are proven. Sugano"s theorem is extended to -Frobenius extensions and their endomorphism rings. In Section 5, the problem of when separable extensions are Frobenius extensions is discussed. A Hopf algebra example and a matrix example are given of finite rank free separable -Frobenius extensions which are not Frobenius in the ordinary sense.     

Entropy and entanglement of an effective two-level atom interacting with two quantized field modes in squeezed displaced fock states

We have studied the influences of ac-Stark shifts on the field quantum entropy, with “squeezed displaced Fock states” (SDFSs) basis. By a unitary transformation we derive a Raman-coupled Hamiltonian perturbatively in coupling constants. The exact results are employed to perform a careful investigation of the temporal evolution of entropy. A factorization of the initial density operator is assumed, with the privileged field mode being in the SDFS. We invoke the mathematical notion of maximum variation of a function to construct a measure for entropy fluctuations. The results show that the effect of the SDFS changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The Rabi oscillation frequency, the collapse and revival times of the atomic coherence are found to have strikingly different photon-intensity dependent than those found previously. The general conclusions reached are illustrated by numerical results.     

On imbalances in oriented tripartite graphs

An oriented tripartite graph is the result of assigning a direction to each edge of a simple tripartite graph. For any vertex x in an oriented tripartite graph D(U,V,W), let d _x ⁺ and d _x ⁻ denote the outdegree and indegree respectively of x. Define $ a_{u_i } = d_{u_i }^ + - d_{u_i }^ - , b_{v_j } = d_{v_j }^ + - d_{v_j }^ - $ a_{u_i } = d_{u_i }^ + - d_{u_i }^ - , b_{v_j } = d_{v_j }^ + - d_{v_j }^ - and $ c_{w_k } = d_{w_k }^ + - d_{w_k }^ - $ c_{w_k } = d_{w_k }^ + - d_{w_k }^ - as the imbalances of the vertices u _i in U, v _j in V and w _k in W respectively. In this paper, we obtain criteria for sequences of integers to be the imbalances of some oriented tripartite graph.     

On Subgroup Separability in Hyperbolic Coxeter Groups

We prove that certain hyperbolic Coxeter groups are separable on their geometrically finite subgroups.     

有限生成的幂零群的共轭分离性质

研究了有限生成的幂零群中元素的共轭分离问题.设ω表示全部素数组成的集合,π是ω的非空真子集,G是有限生成的幂零群,则下述三条等价:(i)如果x和y是G中的任意两个不共轭的元素,则x和y在G的某个有限p-商群中不共轭,其中p∈π;(ii)如果x和y是G中的任意两个不共轭的元素,则x和y在G的某个有限π-商群中不共轭;(iii)G的挠子群T(G)是π-群且G/T(G)是Abel群.同时举例说明:设G是有限生成的无挠幂零群,对于任意素数p,x和y都在G的有限p-商群G/G~p中共轭,但x和y在G中不共轭.     

Separability of the Toda Lattice

We study integrability of the nonperiodic, finite-dimensional Toda Lattice (TL) from the point of view of the Hamilton-Jacobi (HJ) theory of separation of variables. Known to be completely integrable in the sense of Arnol'd-Liouville, the system nonetheless cannot be integrated by the HJ method in the ‘original’ generalized physical position-momenta coordinates. The intrinsic (coordinate-free) characterization method by Benenti provides a tool to investigate the separability of the TL system independently of a local system of coordinates.     

Polyhedral Separability Through Successive LP

We address the problem of discriminating between two finite point sets in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear, but not convex nor concave, and define a descent procedure based on the iterative solution of the LP descent direction finding subproblems.     

关于分离性和同胚关系的一些推广

1963年Norman Levine引入了半开集和半连续函数的概念。1972年S.Gene Crossley等又引入不定函数和前半开函数,定义了半同胚,讨论了一系列的半拓扑性质。以后出现了不少有关半开集和半同胚方面的论文。作者拟在这里进一步引入两类分离性和几种新的同胚,并且指出在一定意义下有些名称应当改变。 首先,我们在这里利用半开集,产生一种分离手段——半开集分离性,从而定义一系列新的拓扑空间,它们之间及它们与T_(i-)型拓扑空间(i=0,1,2,3,4)之间有着一定的联     

The Visual Separability of Plotting Symbols in Scatterplots

Abstract

Which symbols should be used to represent different groups of data in the same scatterplot? Hypotheses are derived to predict which symbol pairs should lead to good separability, based on the contrast of the symbols' visual properties or “features.” In two experiments, experimental scatterplots were shown to subjects on a computer screen; the dependent variable was the decision time to judge which of the two presented symbols was the more frequent one. Analyses of the within-subject effects yielded the following results: (1) Important feature contrasts are brightness, number of line endings, and curvature. (2) Symbols that differ simultaneously in two feature dimensions may be more separable than symbols that differ only in either one. (3) The contrasts between circular symbols and radial line symbols like the plus sign or the asterisk are excellent. Practical applications of these findings are discussed, as well as their contribution to the theory of visual perception.     

Separability of normalizable superintuitionistic propositional logics

The problem of separability of superintuitionistic propositional logics that are extensions of the intuitionistic propositional logic is studied. A criterion of separability of normal superintuitionistic propositional logics, as well as results concerning the completeness of their subcalculi is obtained. This criterion makes it possible to determine whether a normalizable superintuitionistic propositional logic is separable. By means of these results, the mistakes discovered by the author in the proofs of certain statements by McKay and Hosoi are corrected.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 606–615, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-00944.     

On Separability of the Profit Function

The present paper is concerned with deriving conditions on technology which are required for additive separability of the associated profit function. The appropriate representation of technology in this case is the Luenberger shortage function. The paper shows that this function must be simultaneously input-and-output translation homothetic.     

Profinite群的共轭分离性和全形

本文讨论了profinite群的共轭分离性和全形，把关于无限群的结果推广到了profinite群。