Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a "point of no return") at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

Chiral degrees of freedom occur in matter and in electromagnetic fields and constitute an area of research that is experiencing renewed interest driven by recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials. The CISS effect underpins the fact that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision. Any technology that relies on optimal charge transport, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which is presently lacking. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking perspective provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects, and presents a vision for their future roles in enabling room-temperature quantum technologies.

There is increasing interest in the study of chiral degrees of freedom occurring in matter and in electromagnetic fields. Opportunities in quantum sciences will likely exploit two main areas that are the focus of this Review: (1) recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials and (2) rapidly evolving nanophotonic strategies designed to amplify chiral light-matter interactions. On the one hand, the CISS effect underpins the observation that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision and molecular modularity. On the other hand, chiral-optical effects that depend on both spin- and orbital-angular momentum of photons could offer key advantages in all-optical and quantum information technologies. In particular, amplification of these chiral light-matter interactions using rationally designed plasmonic and dielectric nanomaterials provide approaches to manipulate light intensity, polarization, and phase in confined nanoscale geometries. Any technology that relies on optimal charge transport, or optical control and readout, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which has not yet been fully developed. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking Review provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects and presents a vision for their possible future roles in enabling room-temperature quantum technologies.