Related papers: A Graph-Theoretic Approach to Quantum Measurement …
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
It is a well-known fact that measurement incompatibility is a necessary resource to generate nonlocal correlations in usual Bell scenario that typically involves single quantum source. We can provide with some contrasting findings if we…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate…
We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Gr\"{o}tschel, Lov\'{a}sz and…
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…
A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks are shown to belong to the…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
Over 50 years ago, Lov\'{a}sz proved that two graphs are isomorphic if and only if they admit the same number of homomorphisms from any graph [Acta Math. Hungar. 18 (1967), pp. 321--328]. In this work we prove that two graphs are quantum…
We introduce weak oddness $\omega_{\textrm w}$, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph $G$, $\rho(G)\le\omega_{\textrm…
Assuming a well-behaving quantum-to-classical transition, measuring large quantum systems should be highly informative with low measurement-induced disturbance, while the coupling between system and measurement apparatus is "fairly simple"…
In this paper we present a combinatorial machinery, consisting of a graph tower $\overleftarrow \Gamma$ and vector towers $\overleftarrow v$ on $\overleftarrow \Gamma$, which allows us to efficiently describe all invariant measures $\mu =…
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial singular continuous part. A new local Borg--Marchenko…
Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
A rigorous proof of integrability or non-integrability in quantum many-body systems is among the most challenging tasks, as it involves demonstrating the presence or absence of local conserved quantities and deciphering the complex dynamics…
In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a…
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…