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 EITC/QI/QIF Quantum Information Fundamentals:
- Are amplitudes of quantum states always real numbers?
- How the quantum negation gate (quantum NOT or Pauli-X gate) operates?
- Why is the Hadamard gate self-reversible?
- If measure the 1st qubit of the Bell state in a certain basis and then measure the 2nd qubit in a basis rotated by a certain angle theta, the probability that you will obtain projection to the corresponding vector is equal to the square of sine of theta?
- How many bits of classical information would be required to describe the state of an arbitrary qubit superposition?
- How many dimensions has a space of 3 qubits?
- Will the measurement of a qubit destroy its quantum superposition?
- Can quantum gates have more inputs than outputs similarily as classical gates?
- Does the universal family of quantum gates include the CNOT gate and the Hadamard gate?
- What is a double-slit experiment?
View more questions and answers in EITC/QI/QIF Quantum Information Fundamentals