A quantum qubit can indeed represent a superposition of states between 0 and 1, not just the classical states of 0 and 1. In quantum mechanics, the state of a qubit can be described by a mathematical object known as a wavefunction, which is a complex vector in a two-dimensional vector space.
A qubit can exist in a superposition of the basis states |0⟩ and |1⟩, which represent the classical states of 0 and 1, respectively. However, it can also exist in a superposition of states that are linear combinations of |0⟩ and |1⟩. Mathematically, this means the qubit can be in a state α|0⟩ + β|1⟩, where α and β are complex numbers called probability amplitudes. These probability amplitudes determine the probabilities of measuring the qubit in the states |0⟩ and |1⟩.
The key point is that the probability amplitudes α and β can be any complex numbers that satisfy certain normalization conditions. This allows the qubit to exist in a continuum of possible states between |0⟩ and |1⟩. For example, a qubit can be in a state represented by (1/√2)|0⟩ + (1/√2)|1⟩, which corresponds to a superposition where both states |0⟩ and |1⟩ are equally likely when measured.
So, in summary, a quantum qubit can represent a superposition of states between 0 and 1, allowing for a broader range of possibilities than classical bits.