Related papers: Exploring Quantum Contextuality with the Quantum M…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen--Specker and non-Kochen--Specker contextual sets. Traditionally, their representation has…
This article delves into the concept of quantum contextuality, specifically focusing on proofs of the Kochen-Specker theorem obtained by assigning Pauli observables to hypergraph vertices satisfying a given commutation relation. The…
Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined…
We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
This dissertation reviews several recent advances at the intersection of quantum information and holography. In holography, properties of quantum systems admit a gravitational interpretation via the AdS/CFT correspondence. For holographic…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
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…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…
The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…