A projective measurement cannot decrease the von Neumann entropy if the outcome is ignored. However, under certain sound assumptions and using the quantum violation of Leggett-Garg inequalities, we have previously demonstrated that this property is not inherited by a classical simulation of such a measurement process. In the simulation, a measurement erases prior information by partially resetting the system, suggesting that the quantum-state update following a measurement cannot be entirely epistemic. The erasure of information has been proved by assuming that the maximally mixed quantum state corresponds to maximal ignorance of the classical state. A more intricate proof employed the weaker hypothesis that the entropy is finite at some stage of the simulation. In this paper, we focus on the quantum-foundational implications of this theorem. We first provide a simple proof by directly using the second hypothesis. Second, we identify information erasure as the mechanism breaking the time symmetry in ontological theories. This symmetry break has been previously proved by Pusey and Leifer. Third, we show that information erasure, and thus symmetry break, can be avoided by employing a branching similar to many-worlds theory. The information flow and the time asymmetry are transferred to the measurement devices and the subsequent comparison of results, which inherently involve time-asymmetric processes. Thus, causality and the absence of information erasure suggest that measurements have multiple actual outcomes. Similarly, Deutsch and Hayden argued that Bell's theorem leads to the same conclusion if locality is given for granted. We conclude by showing that the problem of the clumsiness loophole in an experimental Leggett-Garg test of macrorealism is mitigated by the information-erasure theorem.

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• Quantum foundations
• Quantum measurements
• Quantum-to-classical transition