Let |ϕ⟩=a|0⟩+b|1⟩ where a and b are nonnegative real numbers. We know that if we measure |ϕ⟩ in the standard basis, the probability of getting a 0 is 925. What is |ϕ⟩?
To find the state vector |ϕ⟩, we can use the fact that the coefficients a and b are nonnegative real numbers. Since the probability of measuring |ϕ⟩ in the standard basis and obtaining a 0 is given as 925, we can write:
|a|^2 = 925,
where |a| denotes the modulus of a. Since the modulus of a nonnegative real number yields the number itself, we have:
a^2 = 925.
Solving this equation for a will give us the value of a. However, since a and b are nonnegative, there are two possible solutions for a, one positive and one negative. So, it is not possible to determine the exact value of a without further information.
Therefore, the state vector |ϕ⟩ cannot be uniquely determined with the given information.