Question

If a quantum state is represented by the vector (1/√2)|0⟩ + (1/√2)|1⟩, what is the probability of measuring the state as |1⟩?

Accepted Answer

In quantum mechanics, a state vector is represented as a linear combination of basis states, such as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex numbers called probability amplitudes. The Born rule states that the probability of measuring a specific outcome is the square of the absolute value of its corresponding amplitude. For the given state (1/√2)|0⟩ + (1/√2)|1⟩, the amplitude associated with the basis state |1⟩ is 1/√2. To find the probability, you calculate the square of the magnitude of this amplitude: |1/√2|^2. Squaring 1/√2 results in (1/√2) multiplied by (1/√2), which equals 1/2. Therefore, the probability of measuring the state as |1⟩ is 0.5, or 50 percent.

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If a quantum state is represented by the vector (1/√2)|0⟩ + (1/√2)|1⟩, what is the probability of measuring the state as |1⟩?

In quantum mechanics, a state vector is represented as a linear combination of basis states, such as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex numbers called probability amplitudes. The Born rule sta....