Unitary transformations are one kind of basic operation which can be performed on qubits. A twodimensional 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. Measurement of the state of the qubit alters the values of a and b. If the state 0⟩ is measured, a is changed to a magnitude of 1 and b is changed to a magnitude of 0 (see magnitude of complex numbers). If the state 1⟩ is measured, b is changed to a magnitude of 1 and a is changed to a magnitude of 0.
For every pure state there exists a measurement that always yields a predictable, constant result. This is why they are called 'pure'. Pure states are constrasted with 'mixed' states, which do not have this property.
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