Introduction to Quantum Computing
The two vectors |0> and |1> are orthonormal means that they are both orthogonal and normalised.
Orthogonal means the vectors are at right angles to each other:
Normalized means the magnitudes of the vectors (i.e. length of the arrow) is equal to 1.
The two vectors |0> and |1> are linearly independent. This means that they cannot be described in terms of each other. However, using both the vectors |0> and |1>, and the rules of addition and multiplication of vectors by scalars, then all possible vectors in 2D space can be described:
Because the vectors |0> and |1> are linearly independent and can be used to describe any vector in 2D space by using vector addition and scalar multiplication, the vectors |0> and |1> form a basis. If the vectors are both orthogonal and normalized, they are called orthonormal basis.
References:
- Orthonormal Basis:
https://learn.qiskit.org/course/ch-states/representing-qubit-states - Qiskit:
https://qiskit.org