Supposing we did want to fully digitize a human WITHOUT merely making a digital xerox? Let us imagine a nano-neuron, a synthetic neuron, injected into the patient’s skull and engineered to observe and study a single biological neuron. It watches, listens, and gradually learns to mimic that neuron’s output by reacting to the same inputs. Over time, it becomes nearly indistinguishable in function. If its output matches the original neuron’s with some acceptable threshold (the importance of this variable cannot be overstated) then for all intents and purposes, it can function as an equivalent prosthetic neuron.
We already know that this idea has at least some precedent in nature. Neurons die all the time with estimates between 75-100k per day [1] yet the continuity of consciousness is preserved. This implies a significant level of built-in redundancy within the brain [2] - a safety net that might allow such a transition to occur without disrupting identity or awareness.
Interesting thought experiment, but I suspect the real answer includes "enough" -- it's not would you be the same if all your neurons were gradually replaced by synthetic neurons, but rather would you be similar enough?