The Annals of Statistics
- Ann. Statist.
- Volume 44, Number 2 (2016), 682-712.
Optimal large-scale quantum state tomography with Pauli measurements
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how these rates can be achieved by a common thresholding approach. Numerical performance of the proposed estimator is also investigated.
Ann. Statist., Volume 44, Number 2 (2016), 682-712.
Received: January 2015
Revised: August 2015
First available in Project Euclid: 17 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H12: Estimation 81P50: Quantum state estimation, approximate cloning
Secondary: 62C20: Minimax procedures 62P35: Applications to physics 81P45: Quantum information, communication, networks [See also 94A15, 94A17] 81P68: Quantum computation [See also 68Q05, 68Q12]
Cai, Tony; Kim, Donggyu; Wang, Yazhen; Yuan, Ming; Zhou, Harrison H. Optimal large-scale quantum state tomography with Pauli measurements. Ann. Statist. 44 (2016), no. 2, 682--712. doi:10.1214/15-AOS1382. https://projecteuclid.org/euclid.aos/1458245732