Related papers: Basic exclusivity graphs in quantum correlations
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
Quantum correlations are the singular, defining resource of quantum information science and metrology, forming the basis of every operational advantage that quantum systems hold over classical ones. Yet exact bounds on these…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
A general treatment of the spectral problem of quantum graphs and tight-binding models in finite Hilbert spaces is given. The direct spectral problem and the inverse spectral problem are written in terms of simple algebraic equations…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…
The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\lceil k/2\rceil $ cycles with consecutive odd lengths. In particular, they showed that this…
Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after…
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional $C^*$-algebras) carry an action of a compact…
The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum…
The question of whether complex numbers play a fundamental role in quantum theory has been debated since the inception of quantum mechanics. Recently, a feasible proposal to differentiate between real and complex quantum theories based on…
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…
Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical…
We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured…
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
In this paper we provide some sufficient conditions for the existence of an odd or even cycle that passing a given vertex or an edge in $2$-connected or $2$-edge connected graphs. We provide some similar conditions for the existence of an…