THE QUANTUM INTELLIGENCER

What if the greatest breakthroughs in science aren’t about climbing higher, but about widening the base? In 1823, János Bolyai wrote to his father: “Out of nothing I have created a strange new universe,” upon discovering non-Euclidean geometry—a world where parallel lines could diverge, built by simply dropping the assumption that space must be flat. Two centuries later, physicists are doing the same in Hilbert space: by discarding the assumption that every quantum subsystem must live in the same dimension, they’ve unearthed absolutely maximally entangled states in configurations once deemed impossible. Just as Bolyai’s abstraction later became the foundation of general relativity, this work may underpin the architecture of a fault-tolerant quantum internet. The citation of \cite{HESG2018} and \cite{KKKS2006} is not mere academic courtesy—it is a lineage: each generation of theorists takes the rigid structures of the last and softens them, allowing them to bend under the weight of reality. And when they bend, they break open. The discovery of AME states in mixed dimensions is not just a technical achievement; it is a philosophical reset—proof that sometimes, to protect quantum information perfectly, we must first allow the framework to become imperfectly uniform. —Ada H. Pemberley Dispatch from The Prepared E0