A generic quantum Wielandt's inequality

In this paper, we provide a generic version of quantum Wielandt's inequality, which gives an optimal upper bound on the minimal length $k$ such that length-$k$ products of elements in a generating system span $M_n(\mathbb{C})$ with probability one. We show that $k$ generically is of order $\Theta(\log n)$, as opposed to the general case, in which the best bound to the date is $O(n^2 \log n)$. Our result implies a new bound on the primitivity index of a random quantum channel. Furthermore, we shed new light on a long-standing open problem for Projected Entangled Pair State, by concluding that almost any translation-invariant PEPS (in particular, Matrix Product State) with periodic boundary conditions on a grid with side length of order $\Omega( \log n )$ is the unique ground state of a local Hamiltonian. We observe similar characteristics for matrix Lie algebras and provide numerical results for random Lie-generating systems.Comment: 13 pages, 6 figure

Finite Fields: Theory and Applications

[no abstract available

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft

An exploratory study of honesty in managerial performance reporting: evidence from Ghana

This exploratory study examines the concept of Honesty (H) in Managerial Performance Reporting (MPR) developing the concept of Honest Managerial Performance Reporting (HPR). It identifies the level of honesty in manager’s performance reporting behaviour and how HPR influences aspects of Firm Performance (FP). The work of Yang (2009) and Evans et al. (2001) provide academic consideration of this area, including insights into how this area may be studied. Practical, real-world examples of such issues are numerous, but the ‘Enron case’ is probably the most well-known (Ndofor et al. 2015). The study utilises datasets of managers, managerial performance reports and companies (Ghana Club 100) in its work and applies a mixed method approach using a variety of research instruments. Several theoretical approaches provide the bedrock for this study and a lens for examining different dimensions of the concept of honesty in MPR. These are Classical agency theory (Jenson & Meckling, 1976), a multi-actor stakeholders model that emanates from Stakeholder theory (Freeman 1984, Yang, 2009), Impression Management (Goffman, 1959), Legitimacy (Deegan, 2002) and Institutional (DiMaggio & Powell, 1983) theories. The thesis explores the level of and factors that influence honesty in managerial performance reporting (HPR). It also determines if HPR has any implication on Firm Performance (FP). From this, four areas of endeavour are formulated, and hypotheses developed to address the issues in each area, and the quest for answers and conclusions to these specifications are pursued. Specifically, the study uses 1) Four experimental constructs to test manager’s voluntary preference for HPR. 2) 265 structured questionnaires to explore the variables affecting HPR. 3) Statistical analysis to examine the relationships between HPR and FP. 4) Vignettes to document HPR practices among Ghana Club 100 companies. The results are the outcomes of the hypotheses and in turn, address the research issues that answer the primary research question leading to conclusions such as: - a) Regarding levels of honesty, managers are partially honest in MPR. b) HPR is affected by a range of factors that include environmental, organisational, economic and individual variables. c) The nature and level of relationship of HPR on FP is that HPR has a significant positive relationship with FP. The clear contribution of this study is that: - a) It uses managers rather than students in HPR studies confirming that managers voluntarily prefer HPR. b) It confirms that HPR is mainly influenced by factors within the control of ‘decision-active’ stakeholders. c) It demonstrates that HPR can be improved if the pay-off for performance related bonuses is deferred rather than paid immediately. d) It provides evidence that HPR has a significant and positive effect on FP. These contributions provide new insight into Managerial Performance, MPR, HPR and the relationship with firm performance, while recognising some limitations. It also makes worthy contributions to our understanding of new contexts

A quantum version of Wielandt's inequality

In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero--error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state