Knotted pictures of entangled states
Qian Shang-Wu, Gu Zhi-Yu · Journal of Physics A Mathematical and General · 2002
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.