Quantum Advantage of Threshold Changeable Secret Sharing Scheme

In TCSS (Threshold Changeable Secret Sharing) scheme, the threshold can be changed to deal with share leakage in the long term. But in classical TCSS, there is no guarantee that old shares are deleted even if the participated parties are honest. So, the changed threshold may not prevent an adversary from reconstructing the secret by the old shares and old threshold number of parties. We show how to tackle this problem quantum mechanically. Namely we can make the changed threshold mandatory through quantum information. So, there is quantum advantage of quantum TCSS over classical ones. We show this by constructing a concrete quantum secret sharing scheme with threshold changeability.