Quantum state tomography for generic pure states

• 来源期刊: 中国科学:物理学 力学 天文学（英文版）
• 年，卷（期）: 2018,（11）
• 页码范围: 1-7
• 页数: 7页
• 语种: 英文

摘要

We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices.We show that a generic pure state in three party Hilbert space HA (×) HB (×)HC,where dim(HA) =2 and dim(HB) =dim(HC),can be uniquely determined by its reduced states on subsystems HA (×) HB and HA (×) HC.Then,we generalize the conclusion to the case that dim(H1) ＞ 2.As a corollary,we show that a generic N-qudit pure quantum state is uniquely determined by only two of its [N+1/2]-particle reduced density matrices.Furthermore,our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D =dN with only O(D) local measurements,which is an improvement compared to the previous known approach that uses O(D log2 D) or O(D log D) local measurements.