Related papers: Algebraic characterisation of one-way patterns
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory…
We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…
Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
We examine the structure of the partition algebra $P_n(\delta)$ over a field $k$ of characteristic $p>0$. In particular, we describe the decomposition matrix of $P_n(\delta)$ when $n<p$ and when $n=p$ and $\delta=p-1$.
Many signals in Nature, technology and experiment have a multi-component structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its…
The theory of path algebras is usually circunscripted to the study of representations, usually linked to finite graphs. In our work, we focus on studying the structure of path algebras over a field associated to arbitrary graphs. We…
We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different…