A good paper for learning about exRec's is this one https://arxiv.org/abs/quant-ph/0504218. Also, rigorous threshold lower bounds are obtained using an adversarial noise model approach.
Could you be more specific by what you mean when you say "the ability to perform quantum measurements with infinite precision"? Several circuit level noise thresholds have been computed where measurement errors are taken into account. Even with measurement errors, thresholds as high as 10^-2 have been reported for depolarizing noise.