Molecular biology explains function of molecules by their geometrical and electronical structures that are mainly determined by utilization of quantum effects in chemistry. However, further quantum effects are not thought to play any significant role in the essential processes of life. On the contrary, consideration of quantum circuits/protocols and organic molecules as software and hardware of living systems that are co-optimized during evolution, may be useful to overcome the difficulties raised by biochemical complexity and to understand the physics of life. In this sense, we review quantum information-theoretic approaches to the process of DNA replication and propose a new model in which 1) molecular recognition of a nucleobase is assumed to trigger an intrabase entanglement corresponding to a superposition of different tautomer forms and 2) pairing of complementary nucleobases is described by swapping intrabase entanglements with interbase entanglements. We examine possible biochemical realizations of quantum circuits/protocols to be used to obtain intrabase and interbase entanglements. We deal with the problem of cellular decoherence by using the theory of decoherence-free subspaces and subsystems. Lastly, we discuss feasibility of the computational or experimental verification of the model and future research directions.