Math Moment

Asked Meta how tgis gives probability 1:

To show that the given expression has a total probability of 1, we need to calculate the sum of the probabilities of each state. In quantum computing, the probability of a state is given by the square of the absolute value of its coefficient.

Let's break down the expression:

(1+i)/2 |0> + 1/√2 |1>

We have two states:

|0> with coefficient (1+i)/2

|1> with coefficient 1/√2

To calculate the probability of each state, we take the square of the absolute value of its coefficient:

State |0>

Probability = |(1+i)/2|^2

= ((1+i)/2) * ((1-i)/2) (multiplying by complex conjugate)

= (1 - i^2)/4

= (1 + 1)/4

= 2/4

= 1/2

State |1>

Probability = |1/√2|^2

= (1/√2) * (1/√2)

= 1/2

Now, let's add the probabilities of both states:

Total Probability = Probability of |0> + Probability of |1>

= 1/2 + 1/2

= 1

Therefore, the total probability of the given expression is indeed 1.

Note: The i in the coefficient of |0> is the imaginary unit, which satisfies i^2 = -1.