Related papers: Non-symmetric GHZ states: weighted hypergraph and …
Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus…
Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite…
Stabilizer states form a ubiquitous family of quantum states that can be graphically represented through the graph state formalism. A fundamental property of graph states is that applying a local complementation - a well-known and…
Hypergraph states are a special kind of multipartite states encoded by hypergraphs relevant in quantum error correction, measurement--based quantum computation, quantum non locality and entanglement. In a series of two papers, we introduce…
Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a…
In this work, we present a novel method to express the stabilizer of a k-uniform complete hypergraph state as a linear combination of local operators. Quantum hypergraph states generalize graph states and exhibit properties that are not…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve…
Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric…
Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…
Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including…
We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU…
The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…
We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered…