Suppose you are given an endless supply of qubits in the state 12√|00⟩+eiϕ2√|10⟩. To estimate the phase angle ϕ, you run Fourier sampling (i.e. Hadamard on each qubit followed by a standard basis measurement) on this state repeatedly. After 100,000,000 measurements, you find that the outcome 01 never occurred. What is ϕ? Please provide your answer in the range ϕ∈[0,2π).
pi -check the chapter 9 edx for answer...
@realstein did you got any other answers?
thnx it worked
no
To estimate the phase angle ϕ, you can use Fourier sampling, which involves applying a Hadamard gate on each qubit followed by a measurement in the standard basis. In this case, you have an endless supply of qubits in the state 1/2√|00⟩ + e^(iϕ)/2√|10⟩.
Since the outcome 01 never occurred in the 100,000,000 measurements, it means that the probability of measuring the outcome 01 is zero. To find the value of ϕ, we can look at the coefficients of the state before measurement.
The state before measurement is 1/2√|00⟩ + e^(iϕ)/2√|10⟩. The coefficient in front of |01⟩ is e^(iϕ)/2.
Since the probability of measuring 01 is zero, the coefficient in front of |01⟩ must be zero. Therefore, e^(iϕ)/2 = 0.
Solving for ϕ, we have e^(iϕ) = 0. Multiplying both sides by 2 gives e^(iϕ) = 0.
The value of e^(iϕ) is never equal to zero for any value of ϕ. Therefore, there is no value of ϕ that satisfies e^(iϕ) = 0.
Hence, it is not possible to estimate the phase angle ϕ in this case using the given information.