Qubit States
A pure qubit state is a linear superposition of the basis states. This means that the qubit can be represented as a linear combination of and :
where α and β are probability amplitudes and can in general both be complex numbers.
When we measure this qubit in the standard basis, the probability of outcome is and the probability of outcome is . Because the absolute squares of the amplitudes equate to probabilities, it follows that α and β must be constrained by the equation
simply because this ensures you must measure either one state or the other.
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