Related papers: A class of positive atomic maps
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
A single linear optical set-up is used to observe an entire family of four-photon entangled states. This approach breaks with the inflexibility of present linear-optical set-ups usually designed for the observation of a particular…
In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer $n$ and a subgroup $G\subseteq \text{GL}_2(\mathbb{Z}/{n}\mathbb{Z})$ with surjective determinant,…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…
Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the…
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement…
How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of…
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
Entanglement in high energy and and nuclear reactions is receiving great attention. A proper description of these reactions uses density matrices, and the express of entanglement in terms of {\it separability}. Quantum tomography bypasses…
We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a…
We construct a scheme for the preparation, pairwise entanglement via exchange interaction, manipulation, and measurement of individual group-II-like neutral atoms (Yb, Sr, etc.). Group-II-like atoms proffer important advantages over alkali…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with…
This short note describes a method to tackle the (bipartite) quantum separability problem. The method can be used for solving the separability problem in an experimental setting as well as in the purely mathematical setting. The idea is to…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The structure of quantum theory assures the discrimination of any possible orthogonal set of states. However, the scenario becomes highly nontrivial in the limited measurement setting and leads to different classes of impossibility, viz.,…