Likely the most compelling possibility for a real zombie apocalypse can come from Neurogenesis. This is, in large thanks, to stem cell research that will soon make it possible for people to regenerate decaying organs. The procedure would work for most organs in our bodies but sadly not on the brain. Essentially, when we die our brain actually begins decaying from the outside in. The outer layers of the brain are pretty important and affect our memory, emotions, decision-making, logic, etc.
Unless you decide to revive someone immediately, their outer brain function will be too far gone to bring them back. In a situation such as this, you could technically have an ordeal science has yet to see. If you could bring someone back to life who simply had the outer layer of their brain erased, they’d still be able to live due to the inner parts operating properly. They would just be a mindless zombie. If someone were to find a way to revive the recently dead using Neurogenesis, they could create an army of undead zombies.