Quantum phases and time crystals in the spatiotemporal-state framework

Investigate whether quantum phases can be extended to the temporal direction and determine whether time crystals can be characterized within the spatiotemporal-state framework.

Background

The paper proposes spatiotemporal quantum states as a unified framework for describing correlations distributed across space and time, but it does not develop an associated theory of phases of matter or temporal phase structure.

The authors explicitly raise the unresolved question of whether quantum phases admit a temporal extension and identify time crystals as a concrete case to be studied using the spatiotemporal-state formalism. These questions are left for future work rather than resolved by the results presented.

References

Moreover, given the notion of quantum states in the temporal direction, it is natural to ask whether the concept of quantum phases can also be extended to time. In particular, it would be interesting to investigate whether time crystals can be characterized within the spatiotemporal-state framework. We leave these questions for future work.

— Unified spatiotemporal quantum states and spatiotemporal entanglement from Kirkwood-Dirac phase space  (2609.24680 - Jia et al., 21 Sep 2026) in Conclusion and outlook