Related papers: Lattice structures for quantum channels
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
We develop a scheme for quantum computation with neutral atoms, based on the concept of "marker" atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic external traps to operate quantum gates between…
A quantum lattice representation (QLA) is devised for the initial value problem of one-dimensional (1D) propagation of an electromagnetic disturbance in a scalar dielectric medium satisfying directly only the two curl equations of Maxwell.…
We develop a framework for Matrix Product Quantum Channels (MPQCs), a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated…
Quantum superchannels are maps whose input and output are quantum channels. Rather than taking the domain to be the space of all linear maps we motivate and define superchannels on the operator system spanned by quantum channels. Extension…
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…
This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is…
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum…
Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of…