Related papers: Dilation Theoretic Parametrizations of Positive Ma…
This paper reviews some characterizations of positive matrices and discusses which lead to useful parametrizations. It is argued that one of them, which we dub the Schur-Constantinescu parametrization is particularly useful. Two new…
In this manuscript, a parametrization of positive matrices together with some of its many applications in quantum information theory is given.
In this note, we discuss dilation-theoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of…
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…
This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention…
A parametrization of density operators for bipartite quantum systems is proposed. It is based on the particular parametrization of the unitary group found recently by Jarlskog. It is expected that this parametrization will find interesting…
The Bloch sphere provides an elegant way of visualizing a qubit. Analogous representation of the simplest composite state of two-qubits has attracted significant attention. Here we present a detailed mathematical analysis of the real-matrix…
A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
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,…
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…
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…
A mixed quantum state is represented by a Hermitian positive semi-definite operator $\rho$ with unit trace. The positivity requirement is responsible for a highly nontrivial geometry of the set of quantum states. A known way to satisfy this…
In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a…
In this paper, we explore the graphical representation of two-qubit entanglement on two Bloch Spheres via stabilizer formalism. We relate the density matrix to the graphical representation on two Bloch Spheres by showing how both may be…
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
We consider bi-linear analogues of $s$-positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite…