Anyone who has heard of quantum computation has probably also heard of decoherence as its worst enemy. While this is true, there are a lot of statements made about decoherence which are not true. For example, we often hear: decoherence makes a quantum system classical, or superposition and entanglement are destroyed after the decoherence time, or any quantum computation should be performed within the decoherence time.

These statements are incorrect. They may be correct under some circumstances, but they are certainly not general.

What is decoherence?

To begin with, let’s be clear what we really mean by decoherence. What makes quantum mechanics so distinct from classical physics is a phenomenon called superposition. Let us take two quantum states $|0rangle$ and $|1rangle$ to represent logical states 0 and 1 of a quantum bit (qubit), respectively. Quantum physics allows having a state like $a|0rangle+b|1rangle$ ($a,b$ being complex numbers), called a superposition state. If this state is measured, the outcome will be either 0 or 1, with probabilities $|a|^2$ and $|b|^2$, respectively. But this is not the same as having a probabilistic mixture of the two states. Before the measurement, the qubit would behave as if it is in both states at the same time, which is not possible classically. Indeed, the power of quantum computation comes from such a classically impossible effect, i.e., superposition.