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Quantum entanglement is a fragile thing. Two friends move to different cities, each carrying a box with one of a pair of gloves: if one box has the left glove, the other has the right. Entangled particles behave similarly, except that until measurement, no one knows which is where.

An electron dives into a crystal, changing its energy as it goes. In an ordinary lattice, it encounters a sequence of allowed bands and forbidden gaps — this is the ABC of semiconductors. But in a quasicrystal, the pattern of atoms never exactly repeats.