Joint quantum-state and measurement tomography with incomplete measurements

作     者：Adam C. Keith Charles H. Baldwin Scott Glancy E. Knill 

作者机构：Applied and Computational Mathematics Division National Institute of Standards and Technology Boulder Colorado 80305 USA Department of Physics University of Colorado Boulder Colorado 80309 USA Center for Theory of Quantum Matter University of Colorado Boulder Colorado 80309 USA 

出 版 物：《Physical Review A》 (Phys. Rev. A)

年 卷 期：2018年第98卷第4期

页      面：042318-042318页

核心收录：

基　　金：Intramural NIST DOC [9999-NIST] Funding Source: Medline 

主　　题：Quantum benchmarking Quantum information with trapped ions Quantum tomography 

摘      要：Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowledge of the system. We present a procedure to simultaneously characterize quantum states and measurements that mitigates systematic errors by use of a single high-fidelity state preparation and a limited set of high-fidelity unitary operations. Such states and operations are typical of many state-of-the-art systems. For this situation we design a set of experiments and an optimization algorithm that alternates between maximizing the likelihood with respect to the states and measurements to produce estimates of each. In some cases, the procedure does not enable unique estimation of the states. For these cases, we show how one may identify a set of density matrices compatible with the measurements and use a semidefinite program to place bounds on the state s expectation values. We demonstrate the procedure on data from a simulated experiment with two trapped ions.