In quantum computing, a qubit can exist in a superposition of states between 0 and 1. This means that a qubit can represent a combination of both the classical states 0 and 1 simultaneously. The exact superposition of states is determined by the quantum state of the qubit, which is represented by a mathematical construct called a quantum state vector.
Mathematically, a qubit can be represented as a linear combination of the basis states |0⟩ and |1⟩, which correspond to the classical states 0 and 1 respectively. The general state of a qubit can be written as:
|ψ⟩ = α|0⟩ + β|1⟩
Here, α and β are complex numbers called probability amplitudes that determine the probability of measuring the qubit in the corresponding classical state. The coefficients α and β must satisfy certain normalization conditions: |α|^2 + |β|^2 = 1.
The superposition property of qubits allows them to exist in a combination of these basis states, represented by complex probability amplitudes. This means that a qubit can be in a state that is a linear combination of |0⟩ and |1⟩, such as:
|ψ⟩ = α|0⟩ + β|1⟩
Where α and β are complex numbers.
When a qubit is measured, it collapses into one of the classical states 0 or 1 with a probability determined by the squared magnitudes of the probability amplitudes. The act of measurement "chooses" one of the classical states with a probability dictated by the quantum state of the qubit.
So, in summary, a qubit can be in a superposition of states between 0 and 1, represented by complex probability amplitudes, but when measured, it will collapse into one of the classical states with a certain probability.