Simple proof of the impossibility of bit commitment in generalized probabilistic theories using cone programming

Bit-commitment is a fundamental cryptographic task where Alice wishes to commit to Bob a bit in such a way that it cannot be changed while simultaneously being hidden from Bob. It is known that ideal bit-commitment is impossible using quantum theory. In this work, we show that it is also impossible in generalised probabilistic theories (GPTs) under a small set of assumptions. In fact, we prove that integer-commitment is impossible using the generality of our proof technique. Our proof relies crucially on a formulation of cheating strategies as cone programs, a natural generalisation of semidefinite programs.