Robin Lyth Hudson (4 May 1940 – 12 January 2021) was a British mathematician notable for his contribution to quantum probability.

Hudson received his Ph.D. from the University of Oxford in 1966 under John T. Lewis with a thesis entitled Generalised Translation-Invariant Mechanics.

He was appointed assistant lecturer at the University of Nottingham in 1964, promoted to a chair in 1985 and served as head of department from 1987 to 1990.

He spent sabbatical semesters in Heidelberg (1978), Austin, Texas (1983), and Colorado Boulder (1996).

An early result,[2] now known as Hudson's theorem in quantum optics, shows that the pure quantum states with positive Wigner quasiprobability distribution are the Gaussian ones.