Related papers: Exploring Quantum Contextuality with the Quantum M…
While entanglement is a cornerstone of quantum theory and holography, quantum correlations arising from superposition, such as quantum discord, offer a broader perspective that has remained largely unexplored in holography. We construct…
We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
Bi-partite entanglement in multi-qubit systems cannot be shared freely. The rules of quantum mechanics impose bounds on how multi-qubit systems can be correlated. In this paper we utilize a concept of entangled graphs with weighted edges in…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…
Contextuality is a hallmark feature of the quantum theory that captures its incompatibility with any noncontextual hidden-variable model. The Greenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextuality that reveal this…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2…
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…