Related papers: A Note on Decomposable Maps on Operator Systems
Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment,…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We extend the theory of equitable decompositions, in which, if a graph has a particular type of symmetry, i.e. a uniform or basic automorphism $\phi$, it is possible to use $\phi$ to decompose a matrix $M$ appropriately associated with the…
This work introduces and systematically studies a new convex cone of PCOP (pairwise copositive). We establish that this cone is dual to the cone of PCP (pairwise completely positive) and, critically, provides a complete characterization for…
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…
In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed `Herman map' is developed.…
Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…
Let H be a complex Hilbert space and denote by Bs(H) the set of all self-adjoint bounded linear operators on H. In this paper we describe the form of all bijective maps (no linearity or continuity is assumed) on Bs(H) which preserve the…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
We suggest a new delooping machine, which is based on recognizing an n-fold loop space by a collection of operations acting on it, like the traditional delooping machines of Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike in the…
Consider the (formal/analytic/algebraic) map-germs Maps(X,(k^p,o)). Let G be the group of right/contact/left-right transformations. I extend the following (classical) results from the real/complex-analytic case to the case of arbitrary…
The purpose of this short note is to clarify and present a general version of an interesting observation by Piani and Mora (Physic. Rev. A 75, 012305 (2007)), linking complete positivity of linear maps on matrix algebras to decomposability…
Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system.…
Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on…
Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key…
This paper proposes an optimized mapping of the FIR filter algorithm that enhances the rate of a reconfigurable computer over a basic mapping previously proposed [1]. It also presents a new interconnection scheme in the reconfigurable part…
Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby CFTs. We show that the…
We show that if $X$ is an $m$-dimensional definable set in $\mathbb{R}^\text{pow}_\text{an}$, the structure of real subanalytic sets with real power maps added, then for any positive integer r there exists a $C^r$-parameterization of X…