Recognition and Teleportation

We study a possible function of brain, in particular, we try to describe several aspects of the process of recognition. In order to understand the fundamental parts of the recognition process, the quantum teleportation scheme[3, 2, 6, 7] seems to be useful. We consider a channel expression of the teleportation process that serves for a simplified description of the recognition process in brain. It is the processing speed that we take as a particular character of the brain, so that the high speed of processing in the brain is here supposed to come from the coherent effects of substances in the brain like quantum computer, as was pointed out by Penrose. Having this in our mind, we propose a model of brain describing its function as follows: The brain system BS =X is supposed to be described by a triple ( B(H), S(H), Λ∗(G) ) on a certain Hilbert space H where B(H)is the set of all bounded operators on H, S(H) is the set of all density operators and Λ∗(G) is a channel giving a state change with a group G. Further we assume the following: (1) BS is described by a quantum state and the brain itself is divided into several parts, each of which corresponds to a Hilbert space so that H =⊕kHk