Related papers: On structural physical approximations and entangle…

We build apon our previous work, the Buckley-\vSivic method for simultaneous construction of families of positive maps on $3 \times 3$ self-adjoint matrices by prescribing a set of complex zeros to the associated forms. Positive maps that…

A class of quantum channels and completely positive maps (CPMs) are introduced and investigated. These, which we call subspace preserving (SP) CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve…

M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital…

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits in each subsystem). Our construction provides a new method of generalization of the…

Here we consider a class of $2\otimes2\otimes d$ chessboard density matrices starting with three-qubit ones which have positive partial transposes with respect to all subsystems. To investigate the entanglement of these density matrices, we…

We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…

Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps…

The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is…

The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a…

Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…

I argue that it would be crucial to have as many channels as possible to understand the physics of electroweak symmetry breaking (EWSB) in next-generation collider experiments. A historic example of the parity violation and the $V-A$…

It has been shown that finding generic Bell states diagonal entanglement witnesses (BDEW) for $d_{1}\otimes d_{2}\otimes ....\otimes d_{n}$ systems exactly reduces to a linear programming if the feasible region be a polygon by itself and…

It is shown that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal. The result is analyzed in detail for the positive projection onto a spin factor.

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…

Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not exceed its initial value during the time…

Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an…

The concept of divisibility of dynamical maps is used to introduce an analogous concept for quantum channels by analyzing the \textit{simulability} of channels by means of dynamical maps. In particular, this is addressed for Lindblad…

We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using…

Complete complementarity relations, as e.g. $P(\rho_{A})^{2} + C(\rho_{A})^{2} + E(|\Psi\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs…

Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives…