- Pure qubit state
In
quantum information processing , a purequbit state is a non-zeroQuantum superposition of two basis states, conventionally written inbra-ket notation notation as 0 angle and 1 angle . Two pure qubit states are physically indistinguishableif 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 anddensity matrix . Also seequantum operation .
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