This paper introduces the unified expression of four Bell bases and uses the composition operation in knot theory to obtain the knotted picture of unitary operators based on Pauli operators, and gives the knotted expressions of 12 inversion relations between the four Bell bases.
From the comparison of the correlation tensor in the theory of quantum networks and the Alexander relation matrix in the theory of knot crystals we find that there is a one-to-one correspondence between four Bell bases and four oriented links of the linkage 4 1 in knot theory. Meanwhile, we show that the inversion relations under the action of Pauli matrices are the same for the four Bell bases and their corresponding links. Similarly we show that there is also a one-to-one correspondence between 2 m GHZ states of m nodes and 2 m oriented links of m components.