Probing Quantum States Over Spacetime Through Interferometry

TL;DR

This paper introduces an interferometry-based framework for defining and analyzing quantum states across spacetime, unifying various formalisms and exploring non-Markovianity and spatiotemporal correlations.

Contribution

It provides an operational, causally agnostic measurement scheme for multipartite quantum states over spacetime, merging density operators, QSOT, and process matrix formalisms.

Findings

Interferometry can implement causally agnostic measurements for spacetime quantum states.

Different quantum dynamics ensembles can produce identical QSOTs, making them indistinguishable via interferometry.

New spatiotemporal correlations from time-reversal symmetry can serve as quantum references.

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.