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A recent no-go theorem (Frauchiger and Renner, 2018) establishes acontradiction from a specific application of quantum theory to a multi-agentsetting. The proof of this theorem relies heavily on notions such as 'knows' or`is certain that'. This has stimulated an analysis of the theorem by Nurgalievaand del Rio (2018), in which they claim that it shows the "[i]nadequacy ofmodal logic in quantum settings" (ibid.). In this paper, we will offer asignificantly extended and refined reconstruction of the theorem in multi-agentmodal logic. We will then show that a thorough reconstruction of the proof asgiven by Frauchiger and Renner requires the reflexivity of access relations(system $\mathsf{\mathbf{T}}$). However, a stronger theorem is possible thatalready follows in serial frames, and hence also holds in systems of\emph{doxastic} logic (such as $\mathsf{\mathbf{KD45}}$). After proving this,we will discuss the general implications for different interpretations ofquantum probabilities as well as several options for dealing with the result.

Quantum information vs.\ epistemic logic: An analysis of the Frauchiger-Renner theorem