Suppose I have a quantum state represented by a Complex vector, arbitrarily:

$[~-0.538, 0.044 - 0.323i, 0.706, 0.044 + 0.323i~]$

With each value in that vector corresponding to some classical state:

$[~ |00\rangle, |01\rangle, |10\rangle, |11\rangle ~]$

What is the correct mathematical formula to derive a probability distribution across possible classical states that could be observed in measurement from this complex vector?

E.g. how do I find individual real values for $p(|00\rangle)$, $p(|01\rangle)$ etc. in this example?


The quantum state is a vector $v$ of unit norm. The probability of measuring outcome $x$ is $\|v_x\|^2$, the squared magnitude of the corresponding coefficient in the vector. Since $v$ has unit norm, these probabilities add up to $1$.

| cite | improve this answer | |
  • $\begingroup$ to check I understand correctly; in my example, p(|01>) = 0.044^2 + (-0.323)^2? $\endgroup$ – Tim Atkinson Dec 16 '16 at 17:24
  • 1
    $\begingroup$ @Atkrye Exactly. $\endgroup$ – Yuval Filmus Dec 16 '16 at 20:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.