does a method exist to distinguish two component link consisting of just two unknots from an unlink?

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Clearly, linking number is not enough as there are links like whitehead. There is the enhanced linking number based on conway polynomial that can distinguish whitehead (and infinite family of such links) from unlink, but do other (families of) 2-links exist that have zero linking number, consist of two unknots and can not be distinguished from unlink by the enhanced linking number? If so, is there any method how to distinguish them? I am not asking to distinguish all the possible 2-links, but just in the subclass that consists of two unknots, I want to distinguish unlink from other type. Thanks!