A natural extension of the information-theoretic Darwinian approach for biological systems is obtained taking into account that biological systems are constituted in their fundamental level by physical systems. Therefore it is through the interaction among physical elementary systems that the biological level is reached after increasing several orders of magnitude the size of the system and only for certain associations of molecules – biochemistry.
In particular, this viewpoint lies in the foundation of the “quantum brain” project established by Hameroff and Penrose (Shadows of the Mind). They tried to lift quantum physical processes associated with microsystems composing the brain to the level of consciousness. Microtubulas were considered as the basic quantum information processors. This project as well the general project of reduction of biology to quantum physics has its strong and weak sides. One of the main problems is that decoherence should quickly wash out the quantum features such as superposition and entanglement. (Hameroff and Penrose would disagree with this statement. They try to develop models of hot and macroscopic brain preserving quantum features of its elementary micro-components.)
However, even if we assume that microscopic quantum physical behavior disappears with increasing size and number of atoms due to decoherence, it seems that the basic quantum features of information processing can survive in macroscopic biological systems (operating on temporal and spatial scales which are essentially different from the scales of the quantum micro-world). The associated information processor for the mesoscopic or macroscopic biological system would be a network of increasing complexity formed by the elementary probabilistic classical Turing machines of the constituents. Such composed network of processors can exhibit special behavioral signatures which are similar to quantum ones. We call such biological systems quantum-like. In the series of works Asano and others (Quantum Adaptivity in Biology From Genetics to Cognition), there was developed an advanced formalism for modeling of behavior of quantum-like systems based on theory of open quantum systems and more general theory of adaptive quantum systems. This formalism is known as quantum bioinformatics.
The present quantum-like model of biological behavior is of the operational type (as well as the standard quantum mechanical model endowed with the Copenhagen interpretation). It cannot explain physical and biological processes behind the quantum-like information processing. Clarification of the origin of quantum-like biological behavior is related, in particular, to understanding of the nature of entanglement and its role in the process of interaction and cooperation in physical and biological systems. Qualitatively the information-theoretic Darwinian approach supplies an interesting possibility of explaining the generation of quantum-like information processors in biological systems. Hence, it can serve as the bio-physical background for quantum bioinformatics. There is an intriguing point in the fact that if the information-theoretic Darwinian approach is right, then it would be possible to produce quantum information from optimal flows of past, present and anticipated classical information in any classical information processor endowed with a complex enough program. Thus the unified evolutionary theory would supply a physical basis to Quantum Information Biology.