The (k, n)-threshold quantum secret sharing scheme is an important and difficult field in quantum information processing and quantum cryptography. In this paper, the (k, n)-threshold quantum secret sharing scheme based on local operations and classical communication (LOCC-QSS) is investigated. Firstly, in order to effectively study the LOCC-QSS scheme, digital and graphical representations of judgement space are introduced creatively. These representations are simple and convenient. Secondly, an algorithm is designed to search optional states for any given k and n. For optional states, the unambiguous probability equals 0 when x participants cooperate (x < k). Thirdly, a method is proposed to decrease the guessing probability. Some schemes which are more secure than existing ones can be obtained further. Last but not least, the conditions of optimal LOCC-QSS schemes are given for the first time. Our research will be helpful for the development of LOCC-QSS scheme.

（k，n）个阈值的量子秘密共享方案是量子信息处理和量子密码学中一个重要而又困难的领域。本文研究了基于本地操作和经典通信（LOCC-QSS）的（k，n）阈值量子秘密共享方案。首先，为了有效地研究LOCC-QSS方案，创造性地引入了判断空间的数字和图形表示。这些表示既简单又方便。其次，设计一种算法来搜索任意给定的k和n的可选状态。对于可选状态，当x个参与者合作时，明确概率等于0 （x  <  k）。第三，提出一种降低猜测概率的方法。可以进一步获得一些比现有方案更安全的方案。最后但并非最不重要的是，首次给出了最佳LOCC-QSS方案的条件。我们的研究将有助于LOCC-QSS方案的发展。