Related papers: On positive maps in quantum information
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
The physically allowed quantum evolutions on a single qubit can be described in terms of their geometry. From a simple parameterisation of unital single-qubit channels, the canonical form of all such channels can be given. The related…
We express the positive partial transpose (PPT) separability criterion for symmetric states of multi-qubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus…
The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from…
Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization…
We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework…
Completely positive transformations play an important role in the description of state changes in quantum mechanics, including the time evolution of open quantum systems. One useful tool to describe them is the so-called Choi isomorphism,…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
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…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
A linear map $L$ from ${\mathbb C}^{n \times n}$ into ${\mathbb C}^{n \times n}$ is called a quantum channel if it is completely positive and trace preserving. The set ${\cal L}_n$ of all such quantum channels is known to be a compact…
By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these…