Recent outstanding theoretical and experimental successes in quantum physics are considered by many to be forging a second quantum revolution. These successes clearly indicate that important quantum technological improvements are on the way. However, many important foundational issues in quantum theory have not yet been clearly resolved, e.g. the quantum measurement problem, the justification of the application of the quantum formalism for macroscopic systems, the possibility of going beyond quantum theory, quantum non-locality, the relativistic treatment of entanglement and an indisputable understanding of the probabilistic structure of Bell's argument. Therefore, nowadays, foundational studies of such problems are immediately relevant.
In many ways, foundational studies continue to drive quantum experimentation and technology, as they have historically, as in the study of entanglement. Moreover, this second quantum revolution has raised new problems such as the role of contextuality in quantum theory, the derivation of this formalism from natural operational and probabilistic principles, and the applicability of the mathematical formalism of quantum theory (especially quantum probability and quantum information) outside of quantum physics, e.g. in decision theory.
We also stress that, for many, some old foundational problems of the greatest importance have been, so to speak, ‘forgotten’. Researchers often proceed pragmatically with the illusion that success in quantum information and technology might be achieved without paying much attention to such problems. History has shown that this approach is always limited, bringing research back to the foundational questions in order to provide a path for continued innovation. In this issue, we shall clearly point to the necessity of quantum foundational studies to accelerate progress in the growing field of quantum engineering. This issue will further strengthen the wave of interest in foundational studies in the quantum community and beyond, bolstering progress in both quantum theory and quantum technology. It represents the views of leading experts in quantum foundations, some of them having close ties with quantum experiment and technology [1–9].
We hope that the reader will enjoy this theme issue, which will be useful to experts working in quantum physics and quantum information theory, ranging from experimentalists to theoreticians, mathematicians and philosophers. A few papers in this issue are devoted specifically to novel applications of the mathematical formalism of quantum theory to modelling the process of decision-making (with the aid of theory of open quantum systems), from cognitive psychology to geology, and should be useful to experts in decision theory in particular.
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