Sample-optimal tomography of quantum states
- LecturerDr. Nengkun Yu (Institute for Quantum Computing University of Waterloo)
Host: Kai-Min Chung - Time2016-09-07 (Wed.) 10:00 ~ 12:00
- LocationAuditorium 107 at IIS new Building
Abstract
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error ϵin trace distance required O(dr2/ϵ2) copies for a d-dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O((dr/δ)ln(d/δ)) copies of ρ to error δ in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr/ϵ2)ln(d/ϵ)) copies suffice to achieve error ϵin trace distance. For fixed d, our measurement can be implemented on a quantum computer in time polynomial in n.
It is a joint work of Jeongwan Haah, Aram W. Harrow, Zhengfeng Ji, Xiaodi Wu, Nengkun Yu