Related papers: Graphical Non-contextual Inequalities for Qutrit S…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
In this paper, we define the quotinet graphs. In particular, we introduce the boundary quotient graphs, admissible boundary quotient graphs and subgraph boundary qoutient graphs. By the property of the quotient spaces, the boundary…
We uncover new features of generalized contextuality by connecting it to the Kirkwood-Dirac (KD) quasiprobability distribution. Quantum states can be represented by KD distributions, which take values in the complex unit disc. Only for…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
We show that the perfect commutation graph is the sufficient tight condition for admitting the noncontextual description of each observable set satisfying it in the yes-no question scenario. With this condition, we propose a method for…
We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed…
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit…
We propose a construction of quantum hypergroups using conditional expectations on compact quantum groups. Using this construction, we describe several series of non-trivial finite-dimensional quantum hypergroups via conditional…
Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has…
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…
We present a derivation and experimental implementation of a dimension-dependent contextuality inequality to certify both the quantumness and dimensionality of a given system. Existing methods for certification of the dimension of quantum…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges…
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…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
The integration of knowledge graphs (KGs) with large language models (LLMs) offers significant potential to improve the retrieval phase of retrieval-augmented generation (RAG) systems. In this study, we propose KG-CQR, a novel framework for…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…