Related papers: Practical construction of positive maps which are …
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence…
Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
Computing $p \rightarrow q$ norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing $p \rightarrow q $ norm for a matrix with nonnegative entries. Here we define an…
We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices.
We study the potential of general quantum operations, Trace-Preserving Completely-Positive Maps (TPCPs), as encoding and decoding mechanisms in quantum authentication protocols. The study shows that these general operations do not offer…
Recently, SyncMap pioneered an approach to learn complex structures from sequences as well as adapt to any changes in underlying structures. This is achieved by using only nonlinear dynamical equations inspired by neuron group behaviors,…
We propose a family of positive maps constructed from a recently introduced class of symmetric measurements. These maps are used to define entanglement witnesses, which include other popular approaches with mutually unbiased bases and…
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…
We present entcalc, a Python and MATLAB package for estimating the geometric entanglement of multipartite quantum states. The package operates as follows: given a multipartite quantum state as input, it outputs an estimate of its geometric…
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction…
This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmetric biquadratic forms, we establish a connection between the…
This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…
Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics, has been recently rediscovered as a new physical resource with potential commercial applications such as, for example,…
Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and…
A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $A = BB^T$. We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking interiors of the CP…
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
In this paper we describe a new connection between UPB (unextendable product bases) and P (positive) maps which are not CP (completely positive). We show that inner automorphisms of the set of P maps which are not CP, produce extremal…