What's the difference between T1 and T2?

I learned that T1 is relaxation time (time from $|1\rangle$ to $|0\rangle$ ) and T2 is coherence time. The relaxation is a specific case of decoherence. What's the difference between them and what's the exact meaning of coherence time T2?

• decoherence
• terminology-and-notation

$\begingroup$ Old question, but I'm adding this as a comment. This online doc very nicely describes T1 and T2 times: mri-q.com/bloch-equations.html $\endgroup$

2 Answers 2

T2 is so-called dephasing time.

It describes how long the phase of a qubit stays intact. In your words, it is time from $|+\rangle= \frac>(|0\rangle + |1\rangle)$ to $|-\rangle= \frac>(|0\rangle - |1\rangle)$ , or conversely.

Just note that both T1 and T2 are not actually "time from state x to state y" but rather decay constants. Probability that a qubit will stay in state $|1\rangle$ after time $t$ is given by formula

Similarly for T2.

Both times T1 and T2 are together called decoherence times.

Slight correction to Martin Vesely's answer: $T_2$ is not the (decay constant) time after which an initial state $|+\rangle$ will necessarily switch to the state $|-\rangle$ . If it were, then error correction would be easy. Instead, it's the (decay constant) time after which an initial state $|+\rangle$ will evolve into an equal classical probabilistic mixture of the $|+\rangle$ and $|-\rangle$ states, so that you can no longer confidently predict the state. That is, it's the autocorrelation time after which the initial and final states become uncorrelated, not negatively correlated.

$\begingroup$ +1 to this answer - a good explanation can be found here as well, I think it is helpful to see the "how do you measure it" and "how the curves typically look like": ocw.mit.edu/courses/mathematics/… $\endgroup$