Related papers: Algebraic structures of multipartite quantum syste…

We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms…

Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge. Most proposed measures do not meet the ``genuine'' requirement, making them unsuitable for…

Entanglement of formation is a fundamental measure that quantifies the entanglement of bipartite quantum states. This measure has recently been extended into multipartite states taking the name $\alpha$-entanglement of formation. In this…

The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a…

In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…

We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…

Multipartite quantum states constitute the key resource for quantum computation. The understanding of their internal structure is thus of great importance in the field of quantum information. This paper aims at examining the structure of…

We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…

We derive hierarchies of separability criteria that identify the different degrees of entanglement ranging from bipartite to genuine multi-partite in mixed quantum states of arbitrary size.

We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…

This paper is an introduction to work motivated by the question "can multipartite entanglement be detected by homological algebra?" We introduce cochain complexes associated to multipartite density states whose cohomology detects…

Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…

Topological states of matter are characterized by nonlocal structures that are naturally encoded in the quantum entanglement of many-body wavefunctions. Topological semimetals are short-range entangled states at weak coupling and their…

Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…

We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…

Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number…

We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication.…

We propose the usage of persistent homologies to characterize multipartite entanglement. On a multi-qubit data set we introduce metric-like measures defined only in terms of bipartite entanglement and then we derive barcodes. We show that…

We consider the separability of rank two quantum states on multiple quantum spaces with different dimensions. The sufficient and necessary conditions for separability of these multiparty quantum states are explicitly presented. A…

A simple algebraic approach to the study of multipartite entanglement for pure states is introduced together with a class of suitable functionals able to detect entanglement. On this basis, some known results are reproduced. Indeed, by…