You are given a source of an unknown qubit state. You make measurements in the computational basis, that is, your measurement is $\{|0\rangle \langle0|,|1\rangle \langle 1|\}$. You observe that you see the outcome zero $30$ times and the outcome one $70$ times out of a hundred measurements. What is your estimate of the absolute value of the probability amplitude of $|0\rangle$ in the superposition?

Any help would be appreciated. Thanks

  • $\begingroup$ To clarify, you want the full probability distribution for the amplitude given the data? Not just a single proportion. $\endgroup$ – AHusain Aug 24 '19 at 0:10
  • $\begingroup$ Do you have any own thoughts on this? $\endgroup$ – Norbert Schuch Aug 24 '19 at 12:03
  • $\begingroup$ Yes, basically an absolute value of the probability amplitude for 0 ket (an estimate is fine). $\endgroup$ – Rahman Turtle Aug 27 '19 at 21:21
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    $\begingroup$ If you have worked it out, just put your answer. You can get yourself a Self-Learner badge. Someone else can expand on it if you miss anything, but it's good to answer your own questions. $\endgroup$ – AHusain Aug 28 '19 at 20:53
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    $\begingroup$ @Ashish the OP asked for the absolute value of the probability amplitude, that is, a real number. $\endgroup$ – Mark S Sep 6 '19 at 13:42

I got the answer 0.547 I got this through the square root of 30/100. as the probability of ket 0 to ket 1 as a fraction.

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    $\begingroup$ For what you missed, imagine you only make 10 measurements and get 0 3 times and 1 7 times. Your procedure would make the same estimate, but you should have more uncertainty. $\endgroup$ – AHusain Sep 4 '19 at 23:05

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