A general framework for consistent logical reasoning in Wigner's friend scenarios: subjective perspectives of agents within a single quantum circuit
It is natural to expect a complete physical theory to have the ability to consistently model agents as physical systems of the theory. In [Nat. Comms. 9, 3711 (2018)], Frauchiger and Renner (FR) claim to show that when agents in quantum theory reason about each other's knowledge in a certain Wi...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
19.09.2022
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Subjects | |
Online Access | Get full text |
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Summary: | It is natural to expect a complete physical theory to have the ability to
consistently model agents as physical systems of the theory. In [Nat. Comms. 9,
3711 (2018)], Frauchiger and Renner (FR) claim to show that when agents in
quantum theory reason about each other's knowledge in a certain Wigner's friend
scenario, they arrive at a logical contradiction. In light of this, Renner
often poses the challenge: provide a set of reasoning rules that can be used to
program quantum computers that may act as agents, which are (a) logically
consistent (b) generalise to arbitrary Wigner's friend scenarios (c)
efficiently programmable and (d) consistent with the temporal order of the
protocol. Here we develop a general framework where we show that every logical
Wigner's friend scenario (LWFS) can be mapped to a single temporally ordered
quantum circuit, which allows agents in any LWFS to reason in a way that meets
all four criteria of the challenge. Importantly, our framework achieves this
general resolution without modifying classical logic or unitary quantum
evolution or the Born rule, while allowing agents' perspectives to be
fundamentally subjective. We analyse the FR protocol in detail, showing how the
apparent paradox is resolved there. We show that apparent logical
contradictions in any LWFS only arise when ignoring the choice of Heisenberg
cut in scenarios where this choice does matter, and taking this dependence into
account will always resolve the apparent paradox. Our results establish that
universal applicability of quantum theory does not pose any threat to
multi-agent logical reasoning and we discuss the implications of these results
for FR's no-go theorem. Moreover, our formalism suggests the possibility of a
truly relational and operational description of Wigner's friend scenarios that
is consistent with quantum theory as well as probability theory applied to
measurement outcomes. |
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DOI: | 10.48550/arxiv.2209.09281 |