You have already learned about basis pairs- a pair of vector that can be used to represent a Qubit in any state. There are an infinte number of basis pairs. Basically, any two vectors that make a 180° or π radians angle with each other on the Bloch Sphere can form a basis pair. The most commonly used basis pairs are |0> and |1>, however, there are a a few other standard basis pairs that are commonly used. In this chapter of the Qiskit Tutorial, you will learn about these standard basis pairs.
|0> and |1> Basis Pairs
The first standard basis pair that we will talk about is |0> and |1>, which also happens to be the most commonly used basis pair. The |0> and |1> basis pairs lie on the Z axis of the Bloch Sphere with |0> lying on the positive Z axis(the ‘north pole’) and |1> lying on the negative Z axis(the ‘south pole’) of the Bloch Sphere.
The diagrams below show the |0> and |1> basis pairs on a Bloch Sphere.
|+> and |-> Basis Pairs
The |+> and |-> basis pairs is another standard basis pair that is used. The |+> and |-> basis pairs lie on the X axis of the Bloch Sphere with |+> lying on the positive X axis and |-> lying on the negative X axis of the Bloch Sphere.
In terms of the |0> and |1> basis pairs, the states |+> and |-> can be described as-
The diagrams below show the |+> and |-> basis pairs on a Bloch Sphere.
|i> and |-i> Basis Pairs
he |i> and |-i> basis pairs is another standard basis pair that is used. The |i> and |-i> basis pairs lie on the Y axis of the Bloch Sphere with |i> lying on the positive Y axis and |-i> lying on the negative Y axis of the Bloch Sphere.
In terms of the |0> and |1> basis pairs, the states |i> and |-i> can be described as-
The diagrams below show the |i> and |-i> basis pairs on a Bloch Sphere.
