Pauli Matrices

Act on (single Qubit)

Properties

• They are Hermetian and unitary
• They anticommute
• They are traceless
• (IMPORTANT PLS REMEMBER)
  In standard basis:
• , for Qubit (bitflip operator)
• , (phase flip operator)
  Similarly, but swapped:
• ,
• ,

idk why I care about these:

• form a basis of
• Hilbert-Schmidt Inner Product satisfies for both from above basis
• Also