Ruling out higher-order interference from purity principles

Abstract

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits, there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the interference pattern has an irreducible dependence. Many authors have wondered why quantum interference is limited to the second level of this hierarchy. Does the existence of higher-order interference violate some natural physical principle that we believe should be fundamental? In the current work we show that such principles can be found which limit interference behaviour to second-order, or "quantum-like", interference, but that do not restrict us to the entire quantum formalism. We work within the operational framework of generalised probabilistic theories, and prove that any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification---four principles that formalise the fundamental character of purity in nature---exhibits at most second-order interference. Hence these theories are, at least conceptually, very "close" to quantum theory. Along the way we show that systems in such theories correspond to Euclidean Jordan algebras. Hence, they are self-dual and, moreover, multi-slit experiments in such theories are described by pure projectors.

18+8 pages. Comments welcome. v2: Minor correction to Lemma 5.1, main results are unchanged

References in corpus (17)

• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Higher-order interference and single-system postulates characterizing quantum theory
• Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule
• The computational landscape of general physical theories
• Dilation of states and processes in operational-probabilistic theories
• Experimental Test of Born's Rule by Inspecting Third-Order Quantum Interference on a Single Spin in Solids
• Terminality implies non-signalling
• Measurement sharpness cuts nonlocality and contextuality in every physical theory
• Leaks: quantum, classical, intermediate, and more
• Entanglement as an axiomatic foundation for statistical mechanics
• Two Roads to Classicality
• The Information Content of Systems in General Physical Theories
• Conservation of information and the foundations of quantum mechanics
• A no-go theorem for theories that decohere to quantum mechanics
• On the ongoing experiments looking for higher-order interference: What are they really testing?

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