A qubit is normally represented as a linear combination of the basis states
and , ie;
(1) |
It is a fundamental property of quantum mechanics that we cannot examine a qubit to determine it's
quantum state, in other words, to find out what and are. Instead, upon measurement,
a qubit collapses into the state with probability
and the state
with probability
, such that;
Because of this requirement, equation (1) can be rewritten as;
where
are real numbers. We can ignore the factor of at
the front of the equation, because it has no observable effects, and we can therefore rewrite
equation (1) as;
(2) |