Existence of an information unit as a postulate of quantum theory
Significance Despite the enormous success of quantum theory, its significance and meaning are still being debated. In particular, the standard postulates of quantum theory are abstract mathematical statements in terms of complex vectors, self-adjoint operators, etc., and as such they lack a clear physical interpretation. For this reason, it is difficult to assess what they say about the structure of the physical world. In this article, we prove that quantum theory can be formulated through four very simple postulates, each having a direct physical and intuitive meaning. Also, our postulates unveil some connections between physics and information that remain hidden in the standard postulates, thus supporting Wheeler’s hypothesis “it from bit.” Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.