Determination of stabilizer states
Xia Wu, Ying‐Hui Yang, Yukun Wang, Qiaoyan Wen, Su‐Juan Qin, Fei Gao · Physical Review A · 2015
The determination of many special types of quantum states has been studied thoroughly, such as the generalized $|\text{GHZ}\ensuremath{\rangle}$ states, stochastic local operations and classical communication equivalent $|W\ensuremath{\rangle}$ states, and Dicke states. In this paper, we study another special entanglement state, that is, stabilizer states, which play an important role in quantum error correcting codes, multipartite purification, and so on. We show that all $n$-qubit stabilizer states are uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices for systems which are the supports of $n$ independent generators of the corresponding stabilizer formalisms.