相关论文: Exclusivity principle, Ramsey theory, and $n$-cycl…

A coloring of a complete bipartite graph is shuffle-preserved if it is the case that assigning a color $c$ to edges $(u, v)$ and $(u', v')$ enforces the same color assignment for edges $(u, v')$ and $(u',v)$. (In words, the induced subgraph…

It is known that a PR-BOX (PR), a non-local resource and $(2\rightarrow 1)$ random access code (RAC), a functionality (wherein Alice encodes 2 bits into 1 bit message and Bob learns one of randomly chosen Alice's inputs) are equivalent…

Let $\left(a_{n}\right)_{n}$ be a strictly increasing sequence of positive integers, denote by $A_{N}=\left\{ a_{n}:\,n\leq N\right\} $ its truncations, and let $\alpha\in\left[0,1\right]$. We prove that if the additive energy…

Imagine a task in which a group of separated players aim to simulate a statistic that violates a Bell inequality. Given measurement choices the players shall announce an output based solely on the results of local operations -- which they…

We reframe the EPR argument through an operational lens, replacing the notion of fixed "elements of reality" with context-indexed conditional states - what's often referred to as a measurement assemblage. This move deliberately sidesteps…

This paper summarises an investigation of the statistical properties of orbits escaping from three different two-degree-of-freedom Hamiltonian systems which exhibit global stochasticity. Each H=H_{0}+eH', with H_{0} integrable and eH' a…

We consider losses in collisions of ultracold molecules described by a simple statistical short-range model that explicitly accounts for the limited lifetime of classically chaotic collision complexes. This confirms that thermally sampling…

Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdos conjectured that the random 2-edge-coloring minimizes the number of…

For a prime $p$ we define the Paley graph to be the graph with the set of vertices $\mathbb{Z}/p\mathbb{Z}$, and with edges connecting vertices whose sum is a quadratic residue. Paley graphs are notoriously difficult to study, particularly…

Zero-error coding encompasses a variety of source and channel problems where the probability of error must be exactly zero. This condition is stricter than that of the vanishing error regime, where the error probability goes to zero as the…

Characterising non-classical quantum phenomena is crucial not only from a fundamental perspective, but also to better understand its capabilities for information processing and communication tasks. In this work, we focus on exploring the…

We show that there is a language in $\mathsf{S}_2\mathsf{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds…

Unlike classical correlations, entanglement cannot be freely shared among multiple parties. This unique feature of quantum systems is known as the monogamy of entanglement. While it holds for all multipartite pure states, its converse --…

Bipartite and tripartite EPR-Bell type systems are examined via joint quasi-probability distributions where elementary probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling…

Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states that as long as $E$ has no Complex…

Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…

We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…

In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…

Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…

A central concept in quantum information processing is genuine multipartite entanglement (GME), a type of correlation beyond biseparability, that is, correlations that cannot be explained by statistical mixtures of partially separable…