If the state of a two-qubit system is given by (1/2 + i/2) |00⟩ + (1/2) |01⟩ – (i/2) |11⟩, what is the probability of observing 01?
Given the state of a two-qubit system as (1/2 + i/2) |00⟩ + (1/2) |01⟩ – (i/2) |11⟩, we can calculate the probability of observing the state |01⟩. To do this, we need to understand the principles of quantum superposition and the measurement process.
In quantum mechanics, a qubit is the fundamental unit of quantum information. It can exist in a superposition of states, represented by a linear combination of basis states. In this case, the basis states are |00⟩, |01⟩, |10⟩, and |11⟩, where the first digit represents the state of the first qubit and the second digit represents the state of the second qubit.
To calculate the probability of observing a particular state, we need to find the amplitude of that state and take the absolute value squared. The amplitude is the coefficient in front of the corresponding basis state. In this case, the amplitude of |01⟩ is 1/2.
To find the probability, we square the amplitude:
P(|01⟩) = |amplitude of |01⟩|^2 = (1/2)^2 = 1/4.
Therefore, the probability of observing the state |01⟩ is 1/4.
To further illustrate this, let's consider an example. Suppose we prepare many copies of the two-qubit system in the given state. If we measure the system in the computational basis, which consists of the basis states |00⟩, |01⟩, |10⟩, and |11⟩, we would expect to observe the state |01⟩ approximately 25% of the time.
The probability of observing the state |01⟩ in the given two-qubit system is 1/4.
Other recent questions and answers regarding Examination review:
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