# Quantum entanglement as topological entanglement

According with Aravind:

• the Hopf link, L2a1, corresponds to the Bell state $$\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$$,
• the Borromean link (L6a4) can be considered as GHZ state $$\frac{1}{\sqrt 2}\big(|000\rangle+|111\rangle\big )$$, and
• the link L6n1 can be associated with a W state $$W=\frac{1}{\sqrt 3}\big(|001\rangle+|010\rangle+100\rangle\big )$$.

But, according Melnikov et. al, we have a different picture: the Borromean link L6a4 is associated with the W state while L6n1 is associated with the GHZ state.

The Hopf Link, or the Bell state:

L6a4, or the GHZ state in Aravind and the W state in Melnikov et al.:

L6n1, or the W state in Aravind and the GHZ state in Melnikov et al.:

I am confused with such different assignments. Could someone clarify the issue?

• Probably a link to the first paper is missing, please add it. Jan 27 at 8:34