Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for
(n,n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of
(t,n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a
(t,n) threshold QSS utilizing
QFT. Later, Kao and Hwang (arXiv:1803.00216) have identified a loophole in the scheme but have not suggested any remedy. In this present study, we have proposed a
(t,n) threshold QSS scheme to share a
d dimensional classical secret. This scheme can be implemented using local operations (such as
QFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.
We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.