Abstract

Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over arbitrary regions in spacetime through a causally agnostic measurement, a measurement scheme that can be consistently implemented independently of the causal relation between the regions. We prove that such measurements can always be implemented with interferometry, also known as the scattering circuit technique, wherein the conventional density operator, the recently developed quantum state over time (QSOT), and the process matrix formalisms smoothly merge. This framework allows for a systematic study of mixed states in the temporal setting, which turn out to be crucial for modeling quantum non-Markovianity. Based on this, we demonstrate that two different ensembles of quantum dynamics can be represented by the same QSOT, indicating that they cannot be distinguished through interferometry. Moreover, our formalism reveals a new type of spatiotemporal correlation between two quantum dynamics that originates from synchronized propagation in time under time-reversal symmetry. We show that quantum systems with such correlation can be utilized as a reference frame to distinguish certain dynamics indistinguishable under time-reversal symmetry.

Quantum theory has long treated space and time differently. Quantum states describe systems at a given moment, while changes that unfold over time are represented separately as quantum processes. Finding a consistent way to describe quantum information across both space and time has remained a fundamental challenge.

A research team, led by Professor Seok Hyung Lie of the Department of Physics at UNIST and Professor Hyukjoon Kwon of the School of Computational Sciences at the Korea Institute for Advanced Study (KIAS) has developed a theoretical framework for measuring quantum states that extend across spacetime. Their work shows that these states can be reconstructed using interferometry, a technique widely used in quantum experiments.

The researchers asked whether such measurements could be made without knowing the causal order between different regions in advance. They defined a causally agnostic measurement as one that remains valid regardless of that order, and proved that any measurement meeting this condition can be carried out through interferometry.

Interferometry uses the wave-like behavior of quantum systems to extract information from the interference between different paths. Applying the technique across space and time provides an experimental basis for describing both within the same framework.

The theory also reveals a limit to what interferometry alone can distinguish. Different quantum dynamics can sometimes produce the same quantum state over time, making them indistinguishable through these measurements.

To address this ambiguity, the team considered an additional quantum system that could serve as a reference. This led them to identify a new form of spatiotemporal correlation, which they call synchronization. When two quantum dynamics evolve in sync, one can provide a temporal reference for the other, allowing certain processes to be distinguished even under time-reversal symmetry.

A simple analogy illustrates the idea. A video of a ball moving through the air may not reveal whether it is playing forward or backward from the trajectory alone. A clock visible in the same frame provides a reference for the direction of time. In the researchers' framework, the additional quantum system serves a similar purpose.

“How to define a quantum state that encompasses both space and time, and how such a state can be measured, have remained important questions in quantum information science and the foundations of quantum theory,” said Professor Lie. “This study approaches the problem through measurement, asking what can actually be learned about a spatiotemporal quantum state from experimental observations.”

Professor Lie added that the framework could help describe and analyze quantum information processes in optical, condensed-matter, and superconducting systems. It may also provide a basis for studying situations in which the timing and location of events are not known in advance, including potential applications in quantum radar and particle-collision experiments.

The study was published in   Physical Review Letters on June 24, 2026. The research was supported by the UNIST 2025 Research Fund, the Institute of Information & Communications Technology Planning & Evaluation (IITP), the National Research Foundation of Korea (NRF), and research funding from the Korea Institute for Advanced Study (KIAS).

Journal Reference

Seok Hyung Lie and Hyukjoon Kwon, “Probing Quantum States over Spacetime through Interferometry,”   Phys. Rev. Lett.,  (2026).