In defense of temporal Tsirelson bound

Abstract

In a recent paper, Chatterjee et al. [Phys. Rev. Lett 135, 220202 (2025)] analyze and experimentally implement a specific unitary evolution of a simple quantum system. The authors refer to this type of dynamics as a "superposition of unitary time evolutions." They claim that such an evolution enables a violation of the temporal Tsirelson bound in the Leggett-Garg scenario, a claim that is supported by their experimental results. In this work, we show that the proposed evolution can be understood within a more conventional framework, without invoking a superposition of evolutions. Furthermore, we demonstrate that the apparent violation of the bound arises because the measured quantities are not consistent with the assumptions of the Leggett-Garg scenario.