A qubit, the basic unit of quantum information, can be in a superposition of two classical states. In other words, a qubit can exist in a combination of two states simultaneously. These two states are typically denoted as |0⟩ and |1⟩, representing the computational basis states of the qubit.
Mathematically, a qubit can be represented by a superposition of these two basis states, expressed as:
|ψ⟩ = α|0⟩ + β|1⟩
Here, α and β are complex probability amplitudes that determine the probabilities of measuring the qubit in the corresponding basis states. The magnitudes of α and β are constrained such that the total probability is equal to 1 (i.e., |α|^2 + |β|^2 = 1). This normalization condition ensures that the probabilities sum to 1 and the qubit state is properly defined.
So, while a qubit can be in a superposition of two basis states, it can only collapse to one of those states upon measurement. The measurement outcome would be probabilistic, with the probabilities determined by the squared magnitudes of the amplitudes α and β.