Quantum mechanics replaced the clockwork certainty of classical physics with something far stranger: a framework in which particles do not follow single, predictable paths but instead exist as clouds ...

Quasiprobability distributions resemble probability distributions but can contain negative and imaginary values. Such distributions represent quantum states as probability distributions over phase ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

Dorje C Brody receives funding from Engineering and Physical Science Research Council (EP/X019926/1) and the John Templeton Foundation (62210). The opinions expressed in this publication are those of ...

Diffusion models generate incredible images by learning to reverse the process that, among other things, causes ink to spread through water. Ask DALL·E 2, an image generation system created by OpenAI, ...