Pure qubit state

In quantum information processing, a pure qubit state is a non-zero Quantum superposition of two basis states, conventionally written in bra-ket notation notation as $|\; 0\; angle$ and $|\; 1\; angle$. Two pure qubit states are physically indistinguishable if and only if they are multiples of each other. Accordingly, a pure qubit state ψ can be written as the sum :$psi\; =\; a\; |\; 0\; angle\; +\; b\; |\; 1\; angle$ where "a" and "b" are complex numbers such that :$1\; =\; sqrt\{|a|^2\; +\; |b|^2\}$.

Geometrically, pure qubit states can be represented by elements of the Bloch sphere.

There are various kinds of physical operation that can be performed on pure qubit states.

* Unitary transformation. These correspond to rotations of the Bloch sphere.

* Standard basis measurement is an operation in which information is gained about the state of the qubit. With probability |"a"|², the result of the measurement will be $|\; 0\; angle$ and with probability |"b"|², it will be $|\; 1\; angle$. Measurement of the state of the qubit alters the values of "a" and "b". For instance, if the state $|\; 0\; angle$ is measured, "a" is changed to 1 (up to phase) and "b" is changed to 0. Strictly speaking, a measurement cannot be regarded as an operation on pure qubit states, since it transforms a pure state into a mixed state.

For a more general discussion of these concepts see pure state and density matrix. Also see quantum operation.