Related papers: Graph states and local unitary transformations bey…
Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively…
The graph state formalism offers strong connections between quantum information processing and graph theory. Exploring these connections, first we show that any graph is a pivot-minor of a planar graph, and even a pivot minor of a…
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical…
We describe the structure of the $n$-qubit Clifford group $C_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
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…
Quantum hypergraph states emerged in the literature as a generalization of graph states, and since then, considerable progress has been made toward implementing this class of genuine multipartite entangled states for quantum information and…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the…
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology,…
The framework of measurement-based quantum computation (MBQC) allows us to view the ground states of local Hamiltonians as potential resources for universal quantum computation. A central goal in this field is to find models with ground…
Graph and hypergraph states are important resource states for realizing universal quantum computation and diverse non-local physical phenomena. However, noise learning in such states is challenging due to their large entanglement and magic.…
We review some results on the equivalence of quantum states under local unitary transformations (LUT). In particular, the classification of two-qubit Schmidt correlated (SC) states under LUT is investigated. By presenting the standard form…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure…
In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both…
Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum…
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…
Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a…