How do quantum symmetries break down — and can you detect it locally?

Quantum systems can break symmetry in a weak sense while preserving it strongly — a recently discovered 'strong-to-weak' phase transition with no classical analogue. This paper builds concrete models in 1D and 2D that undergo this transition, and introduces a local diagnostic that approximates the usual global order parameter using only a small spatial patch, with error shrinking exponentially in patch size. That means experimentalists could detect these exotic phases without full system tomography.