A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events
arXiv:2209.09281 · doi:10.1103/nqbv-6qgr
Abstract
Extended Wigner's Friend Scenarios (EWFSs) go beyond the standard usage of quantum theory, where agents are treated classically, and instead model agents as unitary evolving quantum systems. This has been the subject of several no-go results: Frauchiger and Renner (FR) suggested that quantum agents reasoning using quantum theory will arrive at logical paradoxes, while other results highlight challenges for having an objective notion of measurement events and for causal reasoning in EWFSs. This raises the question: Is it possible to reliably make and test scientific predictions, and consistently reason about the world when applying quantum theory universally without assuming that observed measurement outcomes are absolute? We give a positive answer by developing a general quantum circuit framework for EWFSs. We formalise the concept of Heisenberg cuts by mapping them to distinct channels in a quantum circuit, and prove that FR-type paradoxes can be fully resolved by making explicit the conditioning on the quantum channels that are used in the reasoning process. We provide concrete rules by which quantum agents can reason and make predictions in a logically and causally consistent manner. Our framework describes all perspectives and predictions of an EWFS within a single, well-defined causal structure, although it allows events to be fundamentally subjective. Moreover, we show that an objective notion of measurement events nevertheless emerges in real-world experiments. This demonstrates the possibility of a relational yet operational framework overcoming challenges to scientific reasoning in EWFSs without modifying the Born rule, quantum unitarity, or the axioms of classical logic and probability theory. This enables analysis of different EWFS arguments and provides a platform to consistently extend quantum information methods and studies to Wigner's Friend Scenarios.
29+36 pages. v2: framework significantly generalised, improved clarity, additional results. Results generalised from logical to probabilistic consistency, role of causal structure & absoluteness of events made explicit. Introduced non-superagent structure to identify conditions for emergence of objective events & added theorem on recovery of standard quantum circuits in real-world experiments
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