Quantum Threshold Scheme , no cloning theorem

[Shivam Saluja]

A (k,n) quantum threshold scheme (QTS) as a method to split up an unknown secret quantum state | S > into n pieces (shares) with the restriction that k > n / 2 (for if this inequality were violated, two disjoint sets of players can reconstruct the secret, in violation of the quantum no-cloning theorem).
what is the reason behind the above restriction?

 

[Strilanc]

You should link to the paper you're confused about ( Generalized Quantum Secret Sharing ) instead of just quoting it (also you should actually indicate that you're quoting; otherwise it looks like you know that material already or that you're plagiarising).

I'm not sure exactly what you're asking. The reason $k$ has to be greater than $\frac{n}{2}$ is stated in the quote you included: otherwise you could violate the no-cloning theorem by decoding the secret quantum information two independent times.

Maybe the PI institute's intro page on quantum secret sharing will help?