Entanglement and thermodynamics in general probabilistic theories

Abstract

Since the early works of Einstein-Podolsky-Rosen and Schrödinger, entanglement is universally considered one of the most distinctive and puzzling features of quantum mechanics. In traditional introductions to the topics, entanglement is presented as a consequence of the linear structure of the Hilbert space, which imposes that composite systems must have some pure states - the “entangled states” - that are not the product of pure states of the component systems. But is entanglement just a mathematical accident of the linearity of quantum mechanics, or perhaps a more fundamental feature related to the physical content of the theory? This thesis aims at giving a characterization of entanglement and of the transformations of entangled states only in terms of basic information-theoretic principles, without appealing to the specific details of the Hilbert space formalism of quantum mechanics. The principles used in this characterization provide a new angle on the foundations of thermodynamics, on the definition of entropic quantities, and on the relations between thermodynamics and information theory.