  Environmental decoherence appears to be the biggest obstacle for successful
construction of quantum mind theories. Nevertheless, the quantum physicist
Henry Stapp promoted the view that the mind could utilize quantum Zeno effect
to influence brain dynamics and that the efficacy of such mental efforts would
not be undermined by environmental decoherence of the brain. To address the
physical plausibility of Stapp's claim, we modeled the brain using quantum
tunneling of an electron in a multiple-well structure such as the voltage
sensor in neuronal ion channels and performed Monte Carlo simulations of
quantum Zeno effect exerted by the mind upon the brain in the presence or
absence of environmental decoherence. The simulations unambiguously showed that
the quantum Zeno effect breaks down for timescales greater than the brain
decoherence time. To generalize the Monte Carlo simulation results for any
n-level quantum system, we further analyzed the change of brain entropy due to
the mind probing actions and proved a theorem according to which local
projections cannot decrease the von Neumann entropy of the unconditional brain
density matrix. The latter theorem establishes that Stapp's model is physically
implausible but leaves a door open for future development of quantum mind
theories provided the brain has a decoherence-free subspace.
