The "$S_{n,n}$ conjecture" asserts that there does not exist a simple graph on $n$ vertices with Laplacian spectrum $\{0,1,2,\ldots,n-1\}$ for any integer $n \geq 2$. This conjecture has already been ...

A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k candidates. The parame...

We construct PPT states on $\mathbb{C}^m \otimes\mathbb{C}^n$ that have Schmidt number asymptotically approaching the smaller local dimension. More specifically, we construct a PPT state with Schmidt ...

Entanglement distillation is a fundamental task in quantum information theory. In this work, we prove that Werner states in arbitrary dimension are 2-copy distillable if and only if they are 1-copy di...

Motivated by the equivalent partial-trace formulations of Werner-state distillability [P. Costa Rico, Lett. Math. Phys. 115, 47 (2025); S.-Y. Qi et al., Phys. Rev. A 110, 012406 (2024)], we prove a bi...

A graph with Laplacian matrix $L$ is called Laplacian integral if the eigenvalues of $L$ are all integers, and it is called $\{-1,0,1\}$-diagonalizable if $L$ has a full set of eigenvectors with entri...

Residue number systems based on pairwise relatively prime moduli are a powerful tool for accelerating integer computations via the Chinese Remainder Theorem. We study a structured family of moduli of ...

We introduce a convergent hierarchy of lower bounds on the minimum value of a real form over the unit sphere. The main practical advantage of our hierarchy over the real sum-of-squares (RSOS) hierarch...

A matrix is said to have factor width at most k if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single k×k…

YouTube video by Nathaniel Johnston

A "still Life" is a subset S of the square lattice Z^2 fixed under the transition rule of Conway's Game of Life, i.e. a subset satisfying the following three conditions: 1. No element of Z^2-S has e...

A phoenix is an oscillator in Conway’s Life where every cell dies in every generation. The smallest example is Phoenix 1, which oscillates with period 2 and has a constant population of 12: A…