Related papers: Quantum Hypergraph States: A Review
We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic)…
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of…
The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for…
Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and…
Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
Graph states are versatile resources for quantum computation and quantum-enhanced measurement. Their generation illustrates a high level of control over entanglement. We report on the generation of continuous-variable graph states of atomic…
We study entanglement and non-locality of connected four-qubit hypergraph states. One obtains the SLOCC classification from the known LU-orbits. We then consider Mermin's polynomials and show that all four-qubit hypergraph states exhibit…
The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations.…
Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that,…