This special issue is the second outcome of the International Symposium “Worlds of Entanglement,” held at the Free University of Brussels (VUB), on September 29–30, 2017, which had a follow up at the Institute of Philosophy and Complexity Sciences (IFICC), in Santiago de Chile, on March 7–8, 2019. The event gathered more than 50 scholars from different disciplines, ranging from pure mathematics to visual arts, and from multiple regions of the world, including Argentina, Austria, Canada, Chile, France, Germany, Italy, Japan, Poland and the United States, to animate an interdisciplinary dialogue about fundamental issues of science and society.

‘Entanglement’ is a genuine quantum phenomenon, in the sense that it has no counterpart in classical physics. It was originally identified in quantum physics experiments by considering composite entities made up of two (or more) sub-entities which have interacted in the past but are now sufficiently distant from each other. If joint measurements are performed on the sub-entities when the composite entity is in an ‘entangled state’, then the sub-entities exhibit, despite their spatial separation, statistical correlations (expressed by the violation of ‘Bell inequalities’) which cannot be represented in the formalism of classical physics.

As a consequence of these correlations, the composite entity and its properties cannot be entirely described in terms of the sub-systems and their properties. One typically says that, when entanglement is present, the sub-entities show some kind of non-classical connections, losing their identity, whereas the only possible description is in terms of a ‘global state’ which encodes the properties of all the entangled sub-entities as a whole, as if forming a bigger interconnected single entity (see, e.g., Schrödinger (1935) and Horodecki et al. (2009) and references therein).

After stimulating a lively debate among the founding fathers of quantum theory about its deepest meaning, entanglement and its spectacular implications, e.g., non-separability and contextuality at-a-distance or nonlocality, is nowadays fully employed as a powerful resource in a variety of technological applications, which include quantum cryptography, quantum computation, quantum information tasks, and quantum metrology, to the point that the informational and structural possibilities of quantum systems have become the core of many of todays’ technologies (Dowling and Milburn 2003; Gyongyosi and Imre 2019; Aerts et al. 2019; Wang et al. 2020).

More recently, a growing amount of research has been devoted to identify quantum-theoretic structures, including entanglement, in non-physical domains, such as cognition, biology, ecology, computer and social sciences (see, e.g., Aerts 2009; Khrennikov 2010; Busemeyer and Bruza 2012; Melucci 2015 and references therein). The reason for the appearance of quantum-theoretic structures in these domains, however, has not to be searched in that nature is fundamentally made up of quantum entities at the micro-level but, rather, in that the entities studied in these domains exhibit aspects, when they interact with each other and with an external context, which makes the mathematical formalism(s) of quantum theory more suited than more traditional classical formalisms to represent them, their properties, their states and state transformations, their measurements and measurement statistics.

In particular, it has become increasingly evident that empirical violations of Bell inequalities and therefore quantum and/or quantum-type entanglement are systematically present in human language (see, e.g., Aerts et al. 2019 and references therein) whenever individual concepts combine to form composed conceptual entities, because the former create, in the combination process, meaning connections which cannot be represented within classical probabilistic formalisms, whereas they allow a quantum representation in terms of ‘entangled states’ and ‘entangled measurements’.

The foundations, peculiarities and applications of the notion of entanglement, meant in the broad sense above, has been the main aim of the two symposia. In particular, the present special issue incorporates articles that correspond to lectures at the first or second symposia, as well as invited contributions from scholars that participated in the events and the subsequent discussions. These discussions have indeed fostered interesting collaborations and are now giving birth to new research projects in different parts of the world.

More precisely, this issue includes works covering various aspects of entanglement: foundational questions (Diederik Aerts, Massimiliano Sassoli de Bianchi, Sandro Sozzo, Tomas Veloz, Marek Czachor, Nayla Farouki and Philippe Grangier), its application to modeling (Sandro Sozzo), its relation to social science (Urban Kordeš, Ema Demšar, Norah Bowman, Kathryn Schaffer, Gabriela Barreto and Luk Van Langenhove), and application to Complex Systems (William Lawless). Videos of the lectures can be found at

Worlds of Entanglement’s symposia were the natural continuation of past events organized by the Center Leo Apostel for Interdisciplinary Studies, around interdisciplinary reflection, in particular the “Einstein meets Magritte” Conference (1995), and the “Times of Entanglement” Symposium (2010), which brought together some of the world’s most renowned thinkers.

We hope to make this attractive “Worlds of Entanglement” initiatives further grow, organizing new interesting interdisciplinary meetings in a next coming future.