vector Dirac notation linear algebra psi probability amplitudes quantum state vector probability vector qubit ion quantum mechanical interference bit superposition wave interference
A two-dimensional vector mathematically represents a qubit state. Physicists typically use Dirac notation for quantum mechanical linear algebra, writing |ψ⟩ 'ket psi' for a vector labeled ψ. Because a qubit is a two-state system, any qubit state takes the form α|0⟩ + β|1⟩, where |0⟩ and |1⟩ are the standard basis states, and α and β are the probability amplitudes. If either α or β is zero, the qubit is effectively a classical bit; when both are nonzero, the qubit is in superposition. Such a quantum state vector acts similarly to a (classical) probability vector, with one key difference: unlike probabilities, probability amplitudes are not necessarily positive numbers. Negative amplitudes allow for destructive wave interference.
