2020/09/10 by Nengkun Yu, Yu, Nengkun · 4 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.2009.04610
Comments are welcome. The quantum overlapping tomography part was originally announced in arXiv:1904.03218v3
openalex publication_date 2020/09/10 · arxiv created 2020/09/13 · arxiv updated 2020/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly, we show that the quantum state tomography problem of n-qubit system can be accomplished with O((10n)/(ε2)) copies of the unknown state using Pauli measurements. As a direct application, we studied the quantum overlapping tomography problem introduced by Cotler and Wilczek in Ref. \citeCotler2020. We show that the sample complexity is O(\frac10k⋅log(n\choosek/δ))ε2) for quantum overlapping tomography of k-qubit reduced density matrices among n is quantum system, where 1-δ is the confidential level, and ε is the trace distance error. This can be achieved using Pauli measurements. Moreover, we prove that Ω(\fraclog(n/δ)ε2) copies are needed. In other words, for constant k, joint, highly entangled, measurements are not asymptotically more efficient than Pauli measurements.