Causal classification of spatiotemporal quantum correlations in the absence of active interventions

Abstract

``Why'' questions are ubiquitous in our everyday lives. This innate curiosity has led to monumental scientific methodologies to find the ``because'' -- the key to unlocking ``why''. In search of the true causes behind complex phenomena, we typically employ statistical inference along with appropriate interventions, observing how systems react to various types of interventions. For such sophisticated causal inference, it is crucial to distinguish between the direct causal relations and the indirect causal relations, mediated by a common cause. These causal relationships form two primary causal structures: (i) a temporal structure, in which systems are in the relation of a direct cause, and (ii) a spatial structure, in which systems are in the relation of a common cause. In order to infer causal structures, what types of interventions are necessary? Recent research has revealed quantum advantages in this question; when the systems in question exhibit non-classical characteristics, effective causal inference is possible even without performing interventions actively, in a way that would be impossible classically. Motivated by these pioneering studies, this thesis aims to characterize quantum correlations across space-time in the absence of active interventions by causal classification, which is based on their compatible causal structures. The causal classification of quantum correlations involves examining the incompatibility of observed correlations with spatial and temporal structures. While certifying incompatibility with spatial structures is known to be relatively straightforward, establishing an effective approach for certifying incompatibility with temporal structures has remained challenging. Here, we refer to as atemporality this incompatibility with temporal structures, and introduce an efficient means to certify atemporality, contributing to a complete set of tools for inferring underlying causal structures. This also reveals various properties of atemporality: (1) asymmetry under time reversal, and (2) entanglement does not necessarily imply atemporality, although strong entanglement does imply atemporality. Atemporality thus opens a new aspect of quantum correlations across space-time, distinct from other known spatial quantum correlations such as entanglement. This insight has the potential to spur foundational interest, akin to that seen in the study of spatial quantum correlations.