Leaks: quantum, classical, intermediate, and more

Abstract

We introduce the notion of a leak for general process theories, and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence-leaks to quantum theory. Finally, we show that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory ---a feature missing in standard definitions--- hence, we propose a refined definition and study the resulting notion of purity for quantum, classical and intermediate theories.

23 pages

References in corpus (6)

• Reference frames, superselection rules, and quantum information
• Quantum Darwinism
• A generalized no-broadcasting theorem
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Terminality implies non-signalling
• Two Roads to Classicality

Cited by in corpus (17)

• General probabilistic theories: An introduction
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Entanglement is necessary for emergent classicality in all physical theories
• Reconstructing quantum theory from diagrammatic postulates
• Ruling out higher-order interference from purity principles
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
• Classicality without local discriminability: decoupling entanglement and complementarity
• Two Roads to Classicality
• Dilations and information flow axioms in categorical probability
• Universal structure of objective states in all fundamental causal theories
• Compositional resource theories of coherence
• Purity through Factorisation
• A no-go theorem for theories that decohere to quantum mechanics
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• Complete extension: the non-signaling analog of quantum purification
• Causality in Higher Order Process Theories