In defense of temporal Tsirelson bound

TL;DR

This paper critically examines claims of violating the temporal Tsirelson bound, showing that such violations are due to inconsistent measurements rather than genuine quantum effects, and offers a conventional interpretation.

Contribution

It clarifies the nature of the proposed evolution and demonstrates that the apparent violations stem from measurement inconsistencies, not actual breaches of the bound.

Findings

The evolution can be explained without superpositions of unitaries.

Apparent violations result from measurement assumptions not aligning with the scenario.

Provides a conventional framework for understanding the dynamics involved.

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.