  We discuss foundational issues of quantum information biology (QIB) -- one of
the most successful applications of the quantum formalism outside of physics.
QIB provides a multi-scale model of information processing in bio-systems: from
proteins and cells to cognitive and social systems. This theory has to be
sharply distinguished from "traditional quantum biophysics". The latter is
about quantum bio-physical processes, e.g., in cells or brains. QIB models the
dynamics of information states of bio-systems. It is based on the quantum-like
paradigm: complex bio-systems process information in accordance with the laws
of quantum information and probability. This paradigm is supported by plenty of
statistical bio-data collected at all scales, from molecular biology and
genetics/epigenetics to cognitive psychology and behavioral economics. We argue
that the information interpretation of quantum mechanics (its various forms
were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is
the most natural interpretation of QIB. We also point out that QBIsm (Quantum
Bayesianism) can serve to find a proper interpretation of bio-quantum
probabilities. Biologically QIB is based on two principles: a) adaptivity; b)
openness (bio-systems are fundamentally open). These principles are
mathematically represented in the framework of a novel formalism -- quantum
adaptive dynamics which, in particular, contains the standard theory of open
quantum systems as a special case of adaptivity (to environment).
