Pure Qubit State

$\backslash psi\; =\; a\; |\; 0\; \backslash rangle\; +\; b\; |\; 1\; \backslash rangle$

$1\; =\; \backslash sqrt\{|a|^2\; +\; |b|^2\}$.

• 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 $|\; 0\; \backslash rangle$ and with probability |b|², it will be $|\; 1\; \backslash rangle$. Measurement of the state of the qubit alters the values of a and b. For instance, if the state $|\; 0\; \backslash rangle$ 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.

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