Pure qubit state

In quantum information processing, a pure qubit state is a [linear superposition]? of two basis states, conventionally written | 0> and | 1> (ket 0 and ket 1). A pure qubit state is often written as the sum a| 0> + b| 1>, or as a [column vector]? (a, b) where a and b are the complex amplitudes associated with | 0> and | 1>, respectively. Conventionally the coefficients are normalized, i.e., divided by sqrt(|a|²+|b|²). The vector space in which all pure qubit states lie is the two-dimensional Hilbert space.

[Unitary transformation]?s are one kind of basic operation which can be performed on qubits. A two-dimensional unitary transformation transforms a pure qubit state into another.

Measurements? are another basic operation in which knowledge is gained about the state of the qubit. With probability proportional to |a|², the result of the measurement will be 0 and with probability proportional to |b|², it will be 1. Unless the qubit is in either one of the basis states, there is no way to know in advance what the result will be.

Pure qubit states are contrasted to [mixed qubit state]?s, which are a probabilistic mixture of pure states.