scholarly journals LOCC protocols with bounded width per round optimize convex functions

2021 ◽  
pp. 2150013
Author(s):  
Debbie Leung ◽  
Andreas Winter ◽  
Nengkun Yu
Keyword(s):  
Convex Functions ◽  
Convex Combination ◽  
Local System ◽  
Global Dimension ◽  
Coarse Grained ◽  
State Transformation ◽  
Convex Decomposition ◽  
Dimension Formula ◽  
State Discrimination ◽  
Output Dimension

We start with the task of discriminating finitely many multipartite quantum states using LOCC protocols, with the goal to optimize the probability of correctly identifying the state. We provide two different methods to show that finitely many measurement outcomes in every step are sufficient for approaching the optimal probability of discrimination. In the first method, each measurement of an optimal LOCC protocol, applied to a [Formula: see text]-dimensional local system, is replaced by one with at most [Formula: see text] outcomes, without changing the probability of success. In the second method, we decompose any LOCC protocol into a convex combination of a number of “slim protocols” in which each measurement applied to a [Formula: see text]-dimensional local system has at most [Formula: see text] outcomes. To maximize any convex functions in LOCC (including the probability of state discrimination or fidelity of state transformation), an optimal protocol can be replaced by the best slim protocol in the convex decomposition without using shared randomness. For either method, the bound on the number of outcomes per measurement is independent of the global dimension, the number of parties, the depth of the protocol, how deep the measurement is located, and applies to LOCC protocols with infinite rounds, and the “measurement compression” can be done “top-down” — independent of later operations in the LOCC protocol. The second method can be generalized to implement LOCC instruments with finitely many classical outcomes: if the instrument has [Formula: see text] coarse-grained final measurement outcomes, global input dimension [Formula: see text] and global output dimension [Formula: see text] for [Formula: see text] conditioned on the [Formula: see text]th outcome, then one can obtain the instrument as a convex combination of no more than [Formula: see text] slim protocols; that is, [Formula: see text] bits of shared randomness suffice.

scholarly journals Classification of pointed fusion categories of dimension p3 up to weak Morita Equivalence

2020 ◽  
pp. 2140008
Author(s):  
Kevin Maya ◽  
Adriana Mejía Castaño ◽  
Bernardo Uribe
Keyword(s):  
Complete Classification ◽  
Global Dimension ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Fusion Categories ◽  
Dimension Formula ◽  
Equivalent Categories

We give a complete classification of pointed fusion categories over [Formula: see text] of global dimension [Formula: see text] for [Formula: see text] any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension [Formula: see text] and we determine which of these equivalence classes have equivalent categories of modules.

An Upper Bound for the w-Weak Global Dimension of Pullbacks

2021 ◽  
Vol 28 (04) ◽  
pp. 689-700
Author(s):  
Jin Xie ◽  
Gaohua Tang
Keyword(s):  
Commutative Ring ◽  
Upper Bound ◽  
Global Dimension ◽  
Factor Ring ◽  
Dimension Formula ◽  
Milnor Square

Let [Formula: see text] be a commutative ring with identity and [Formula: see text] an ideal of [Formula: see text]. We introduce and study the [Formula: see text]-weak global dimension [Formula: see text] of the factor ring [Formula: see text]. Let [Formula: see text] be a [Formula: see text]-linked extension of [Formula: see text], and we also introduce the [Formula: see text]-weak global dimension [Formula: see text] of [Formula: see text]. We show that the ring [Formula: see text] with [Formula: see text] is exactly a field and the ring [Formula: see text] with [Formula: see text] is exactly a [Formula: see text]. As an application, we give an upper bound for the [Formula: see text]-weak global dimension of a Cartesian square [Formula: see text]. More precisely, if [Formula: see text] is [Formula: see text]-linked over [Formula: see text], then [Formula: see text]. Furthermore, for a Milnor square [Formula: see text], we obtain [Formula: see text].

scholarly journals Convex Combination Inequalities of the Line and Plane

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zlatko Pavić ◽  
Shanhe Wu ◽  
Štefanija Klarić
Keyword(s):  
Convex Functions ◽  
Convex Combination ◽  
Main Idea ◽  
Higher Dimensions ◽  
The Given

The paper deals with convex combinations, convex functions, and Jensen’s functionals. The main idea of this work is to present the given convex combination by using two other convex combinations with minimal number of points. For example, as regards the presentation of the planar combination, we use two trinomial combinations. Generalizations to higher dimensions are also considered.

scholarly journals Convergence Rate Analysis of the Proximal Difference of the Convex Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Xueyong Wang ◽  
Ying Zhang ◽  
Haibin Chen ◽  
Xipeng Kou
Keyword(s):  
Convergence Rate ◽  
Convex Function ◽  
Objective Function ◽  
Convex Functions ◽  
Objective Function Value ◽  
Convex Decomposition ◽  
Rate Analysis ◽  
Difference Of Convex ◽  
The Difference ◽  
Convergence Rate Analysis

In this paper, we study the convergence rate of the proximal difference of the convex algorithm for the problem with a strong convex function and two convex functions. By making full use of the special structure of the difference of convex decomposition, we prove that the convergence rate of the proximal difference of the convex algorithm is linear, which is measured by the objective function value.

scholarly journals On a Subclass of Harmonic Convex Functions of Complex Order

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
N. Magesh ◽  
S. Mayilvaganan
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Closure Property ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Distortion Bounds ◽  
Order Coefficient ◽  
Harmonic Convex

We introduce and study a subclass of harmonic convex functions of complex order. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are determined for functions in this class. Further, we obtain the closure property of this class under integral operator.

A Totally Relaxed, Self-Adaptive Subgradient Extragradient Method for Variational Inequality and Fixed Point Problems in a Banach Space

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Adeolu Taiwo ◽  
Timilehin Opeyemi Alakoya ◽  
Oluwatosin Temitope Mewomo ◽  
Qiao-Li Dong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Convex Functions ◽  
Convex Combination ◽  
Extragradient Method ◽  
Strong Convergence Theorem ◽  
Subgradient Extragradient Method ◽  
Feasible Set ◽  
Self Adaptive

Abstract In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding a common solution of a Variational Inequality Problem (VIP) and the fixed point of quasi-nonexpansive mapping in a 2-uniformly convex and uniformly smooth Banach space. The TRSSEM does not require the computation of projection onto the feasible set of the VIP; instead, it uses a projection onto a finite intersection of sub-level sets of convex functions. The advantage of this is that any general convex feasible set can be involved in the VIP. We also introduce a modified TRSSEM which involves the projection onto the set of a convex combination of some convex functions. Under some mild conditions, we prove a strong convergence theorem for our algorithm and also present an application of our theorem to the approximation of a solution of nonlinear integral equations of Hammerstein’s type. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our algorithm is simple and easy to implement for computation.

Support Points of the Class of Close-to-Convex Functions

1976 ◽  
Vol 19 (2) ◽  
pp. 177-179 ◽  
Author(s):  
E. Grassmann ◽  
W. Hengartner ◽  
G. Schober
Keyword(s):  
Linear Space ◽  
Convex Functions ◽  
Dual Space ◽  
Convex Combination ◽  
Holomorphic Functions ◽  
Support Point ◽  
The Other ◽  
Support Points ◽  
Proper Convex ◽  
Compact Convergence

Let H(U) be the linear space of holomorphic functions on U = {z:|z|<1} endowed with the topology of compact convergence, and denote by H′(U) its topological dual space. Let be a compact subset of H(U) and ƒ∈F. We say ƒ is a support point of if there exists an L∈H'(U), non-constant on , such that On the other hand, ƒ is an extreme point of if ƒ is not a proper convex combination of two other points of .

The Alteration of the Pore Spaces in Sandstones

1973 ◽  
Vol 31 ◽  
pp. 210-211
Author(s):  
R. E. Ferrell ◽  
G. G. Paulson
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
The Other ◽  
Coarse Grained ◽  
Depositional Fabric ◽  
Soluble Components ◽  
Scanning Electron ◽  
Shape And Size

The pore spaces in sandstones are the result of the original depositional fabric and the degree of post-depositional alteration that the rock has experienced. The largest pore volumes are present in coarse-grained, well-sorted materials with high sphericity. The chief mechanisms which alter the shape and size of the pores are precipitation of cementing agents and the dissolution of soluble components. Each process may operate alone or in combination with the other, or there may be several generations of cementation and solution.The scanning electron microscope has ‘been used in this study to reveal the morphology of the pore spaces in a variety of moderate porosity, orthoquartzites.

On the Origin of the Microscystalline Structure in Rapidly Solidified IN-100 Powder

1977 ◽  
Vol 35 ◽  
pp. 260-261
Author(s):  
J. M. Walsh ◽  
K. P. Gumz ◽  
J. C. Whittles ◽  
B. H. Kear
Keyword(s):  
The Other ◽  
Coarse Grained ◽  
Microcrystalline Structure ◽  
Routine Examination ◽  
Atomization Process ◽  
Centrifugal Atomization ◽  
Splat Quenching ◽  
Powder Particles ◽  
Dendritic Microstructures ◽  
Rapidly Solidified

During a routine examination of the microstructure of rapidly solidified IN-100 powder, produced by a newly-developed centrifugal atomization process1, essentially two distinct types of microstructure were identified. When a high melt superheat is maintained during atomization, the powder particles are predominantly coarse-grained, equiaxed or columnar, with distinctly dendritic microstructures, Figs, la and 4a. On the other hand, when the melt superheat is reduced by increasing the heat flow to the disc of the rotary atomizer, the powder particles are predominantly microcrystalline in character, with typically one dendrite per grain, Figs, lb and 4b. In what follows, evidence is presented that strongly supports the view that the unusual microcrystalline structure has its origin in dendrite erosion occurring in a 'mushy zone' of dynamic solidification on the disc of the rotary atomizer.The critical observations were made on atomized material that had undergone 'splat-quenching' on previously solidified, chilled substrate particles.

Correlation between dislocation, grain boundary and interface of duplex SS in stress corrosion cracking(SCC)

1990 ◽  
Vol 48 (4) ◽  
pp. 928-929
Author(s):  
Wang Zheng-fang ◽  
Z.F. Wang
Keyword(s):  
Stainless Steel ◽  
Thermal Cycle ◽  
Secondary Phase ◽  
Corrosion Cracking ◽  
Coarse Grained ◽  
Test Environment ◽  
Fine Grained ◽  
Evaluation Test ◽  
Welding Thermal Cycle ◽  
Micro Analysis

The main purpose of this study highlights on the evaluation of chloride SCC resistance of the material,duplex stainless steel,OOCr18Ni5Mo3Si2 (18-5Mo) and its welded coarse grained zone(CGZ).18-5Mo is a dual phases (A+F) stainless steel with yield strength:512N/mm2 .The proportion of secondary Phase(A phase) accounts for 30-35% of the total with fine grained and homogeneously distributed A and F phases(Fig.1).After being welded by a specific welding thermal cycle to the material,i.e. Tmax=1350°C and t8/5=20s,microstructure may change from fine grained morphology to coarse grained morphology and from homogeneously distributed of A phase to a concentration of A phase(Fig.2).Meanwhile,the proportion of A phase reduced from 35% to 5-10°o.For this reason it is known as welded coarse grained zone(CGZ).In association with difference of microstructure between base metal and welded CGZ,so chloride SCC resistance also differ from each other.Test procedures:Constant load tensile test(CLTT) were performed for recording Esce-t curve by which corrosion cracking growth can be described, tf,fractured time,can also be recorded by the test which is taken as a electrochemical behavior and mechanical property for SCC resistance evaluation. Test environment:143°C boiling 42%MgCl2 solution is used.Besides, micro analysis were conducted with light microscopy(LM),SEM,TEM,and Auger energy spectrum(AES) so as to reveal the correlation between the data generated by the CLTT results and micro analysis.

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