You can approximate any analog value to arbitrary precision using a (by nature binary) Turing Machine, therefore you can bring the loss of information as low as needed.
The question is whether the brain offers a more complete framework than all the models of computation we know today (which are equivalent to one another). To put it another way : is there a function that the brain can compute that a Turing Machine cannot. We know of no such function now, but have ruled out yet that there is none, although most computer scientist agree with the Church-Turing hypothesis.
But this is effectively begging the question. If you assume that reality can be completely described by functions that compute on natural numbers, then obviously anything within reality, including consciousness, can be simulated by a Turing machine.
Unless I've missed something, it's not actually been shown that the universe itself is Turing-computable, therefore there's no reason to assume everything within the universe could be equivalently simulated on a Turing machine.
It could also be that in theory, consciousness is Turing computable, but not in practice. For example just computing a protein fold for 1 millisecond takes hundreds of ASICs days of compute time. This might give some clue that complex physical wetware processes are not able to be efficiently simulated in real time on any realistic Turing machine.
The question is whether the brain offers a more complete framework than all the models of computation we know today (which are equivalent to one another). To put it another way : is there a function that the brain can compute that a Turing Machine cannot. We know of no such function now, but have ruled out yet that there is none, although most computer scientist agree with the Church-Turing hypothesis.