Related papers: A Graph-Theoretic Approach to Quantum Measurement …
Lov\'asz (1967) showed that two graphs $G$ and $H$ are isomorphic if, and only if, they are homomorphism indistinguishable over all graphs, i.e., $G$ and $H$ admit the same number of number of homomorphisms from every graph $F$.…
We introduce a family of conformal invariants associated to a smooth metric measure space which generalize the relationship between the Yamabe constant and the best constant for the Sobolev inequality to the best constants for…
Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce…
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology,…
Rigidity theory enables us to specify the conditions of unique localizability in the cooperative localization problem of wireless sensor networks. This paper presents a combinatorial rigidity approach to measure (i) generic rigidity and…
We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute…
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…
A graph $G$ is called self-ordered (a.k.a asymmetric) if the identity permutation is its only automorphism. Equivalently, there is a unique isomorphism from $G$ to any graph that is isomorphic to $G$. We say that $G=(V,E)$ is robustly…
We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field. We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms…
We present graphs of information versus disturbance for general quantum measurements of completely unknown states. Each piece of information and disturbance is quantified by two measures: (i) the Shannon entropy and estimation fidelity for…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and…
The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This property is particularly useful for comparing datasets that…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
We consider two-dimensional N=(2,2) supersymmetric gauge theory on discretized Riemann surfaces. We find that the discretized theory can be efficiently described by using graph theory, where the bosonic and fermionic fields are regarded as…
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is…