Qubit

• The quantum state of a qubit is a vector of unit length in a 2-dimensional complex vector space known as state space. It is typically represented as α|0⟩ + β|1⟩.

  • |0⟩ and |1⟩ represent the two standard basis vectors of R^2.

  • |α|^2 + |β|^2 = 1

  • α and β can be complex numbers.

• It is impossible to directly observe the state of a qubit.

• When a qubit is measured, the qubit collapses to either |0⟩ or |1⟩ with probabilities |α|^2 and |β|^2 respectively.

  • This is a fundamental consequence of physics. If this were not the case, infinite information could be encoded in a single qubit.