# Why should we use density matrices to simulate quantum systems with noise?

Why we should use density matrices to simulate quantum systems with noise?

I found that the any QEC circuit is included by some quantum gates just like normal cases, which means the state vector can also be used to simulate it, but all of the simulator only can realize noise model with density matrix, can someone help me with that?

Noise effects introduce classical uncertainty in what the underlying state is. A mixed state is a statistical ensemble of several quantum states $$|\psi_i\rangle$$ (not necessarily orthogonal), with respective probabilities $$p_i$$.