Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking
an efficient way. Given a bipartite quantum state of interest free entanglement can be …

Many-body quantum systems can be characterized using the notions of k-separability and
entanglement depth. A quantum state is k-separable if it can be expressed as a mixture of k …

A construction of genuinely entangled multipartite quantum states based on the group theory
is presented. Analyzed states resemble the Dicke states, whereas the interactions occur only …

We provide a systematic method for nonlinear entanglement detection based on trace
polynomial inequalities. In particular, this allows us to employ multipartite witnesses for the …

From a practical perspective it is advantageous to develop methods that verify entanglement
in quantum states with as few measurements as possible. In this paper we investigate the …

We describe a framework for the controllability analysis of networks of $ n $ quantum
systems of an arbitrary dimension $ d $,{\it qudits}, with dynamics determined by …

We present positive maps and matrix inequalities for variables from the positive cone. These
inequalities contain partial transpose and reshuffling operations, and can be understood as …

Computationally intractable tasks are often encountered in physics and optimization. They
usually comprise a cost function to be optimized over a so-called feasible set, which is …

We investigate the entanglement properties in the symmetric subspace of $ N $-partite $ d $-
dimensional systems (qudits). For diagonal symmetric states, we show that there is no …

In this work we examine quantum states which have non-negative amplitudes (in a fixed
basis) and the channels which preserve them. These states include the ground states of …