Oxford, where the real and the unreal jostle in the streets, where windows open into other worlds…

So wrote Philip Pullman, author of The Golden Compass and its sequels. In the series, a girl wanders from the Oxford in another world to the Oxford in ours.

I’ve been honored to wander Oxford this fall. Visiting Oscar Dahlsten and Jon Barrett, I’ve been moonlighting in Vlatko Vedral’s QI group. We’re interweaving 21^st-century knowledge about electrons and information with a Victorian fixation on energy and engines. This research program, quantum thermodynamics, should open a window onto our world.

A new world. At least, a world new to the author.

To study our world from another angle, Oxford researchers are jostling the unreal. Oscar, Jon, Andrew Garner, and others are studying generalized probabilistic theories, or GPTs.

What’s a specific probabilistic theory, let alone a generalized one? In everyday, classical contexts, probabilities combine according to rules you know. Suppose you have a 90% chance of arriving in London-Heathrow Airport at 7:30 AM next Sunday. Suppose that, if you arrive in Heathrow at 7:30 AM, you’ll have a 70% chance of catching the 8:05 AM bus to Oxford. You have a probability 0.9 * 0.7 = 0.63 of arriving in Heathrow at 7:30 and catching the 8:05 bus. Why 0.9 * 0.7? Why not 0.9^0.7, or 0.9/(2 * 0.7)? How might probabilities combine, GPT researchers ask, and why do they combine as they do?

Not that, in GPTs, probabilities combine as in 0.9/(2 * 0.7). Consider the 0.9/(2 * 0.7) plucked from a daydream inspired by this City of Dreaming Spires. But probabilities do combine in ways we wouldn’t expect. By entangling two particles, separating them, and measuring one, you immediately change the probability that a measurement of Particle 2 yields some outcome. John Bell explored, and experimentalists have checked, statistics generated by entanglement. These statistics disobey rules that govern Heathrow-and-bus statistics. As do entanglement statistics, so do effects of quantum phenomena like discord, negative Wigner functions, and weak measurements. Quantum theory and its contrast with classicality force us to reconsider probability.
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