Related papers: Tensor invariants for multipartite entanglement cl…
Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs). Creating reliable, large-scale multipartite entanglement requires…
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…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
Entanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially…
Entanglement between three or more parties exhibits a realm of properties unknown to two-party states. Bipartite states are easily classified using the Schmidt decomposition. The Schmidt coefficients of a bipartite pure state encompass all…
We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case,…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a…
Despite multipartite entanglement being a global property of a quantum state, a number of recent works have made it clear that it can be quantified using only local measurements. This is appealing because local measurements are the easiest…
In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as…
We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants,…
Entanglement is one of the key feature of quantum world and any entanglement measure must satisfy some basic laws. Most important of them is the invariance of entanglement under local unitary operations. We show that this is no longer true…
Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this work,…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite…
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori,…
We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of…
Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state,…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
The existence of non-local quantum correlations is certainly the most important specific property of the quantum world. However, it is a challenging task to distinguish correlations of classical origin from genuine quantum correlations,…
Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and…