In quantum mechanics, when you measure the state of a qubit, you obtain a specific outcome corresponding to one of its basis states. The act of measurement causes the quantum state to "collapse" into one of those basis states with a certain probability determined by the amplitudes in the wavefunction.
Let's consider a simple example with a qubit. The qubit can be in a superposition of two basis states, conventionally denoted as |0⟩ and |1⟩. The wavefunction of the qubit can be expressed as:
ψ = α|0⟩ + β|1⟩,
where α and β are complex probability amplitudes that satisfy the normalization condition |α|^2 + |β|^2 = 1.
When you perform a measurement on the qubit, you obtain either |0⟩ or |1⟩ with probabilities determined by the magnitudes of α and β. The probability of measuring |0⟩ is |α|^2, and the probability of measuring |1⟩ is |β|^2.
However, after the measurement, the quantum state collapses into the measured basis state. For example, if you measure |0⟩, the qubit's state becomes |0⟩, and if you measure |1⟩, the qubit's state becomes |1⟩. The act of measurement disrupts the superposition and causes the qubit to "choose" one of the basis states.
It's important to note that the measurement outcome is probabilistic. The probabilities of obtaining different outcomes are determined by the amplitudes in the wavefunction. This probabilistic nature is inherent to quantum mechanics and distinguishes it from classical physics, where measurements typically yield deterministic results.
In quantum computing, the ability to manipulate and measure qubits in controlled ways is crucial for performing computations. Various quantum algorithms and protocols utilize the principles of superposition and measurement to achieve computational advantages for specific tasks.
To gain a deeper understanding of quantum state, measurement, and related concepts, I recommend studying introductory textbooks on quantum mechanics and quantum computing. Additionally, solving exercises and working through examples will help solidify your understanding of these fundamental concepts in quantum computing.