title: Quantum State Tomography via Reduced Density Matrices.
abstract: Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.
authors.affiliation: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.|Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Tao
authors.initials: T
authors.lastname: Xin
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Dawei
authors.initials: D
authors.lastname: Lu
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada.
authors.forename: Joel
authors.initials: J
authors.lastname: Klassen
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia.|Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada.
authors.forename: Nengkun
authors.initials: N
authors.lastname: Yu
authors.affiliation: Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia.|State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, 100190 Beijing, China.
authors.forename: Zhengfeng
authors.initials: Z
authors.lastname: Ji
authors.affiliation: Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland, USA.
authors.forename: Jianxin
authors.initials: J
authors.lastname: Chen
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Xian
authors.initials: X
authors.lastname: Ma
authors.affiliation: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
authors.forename: Guilu
authors.initials: G
authors.lastname: Long
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada.|Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada.
authors.forename: Bei
authors.initials: B
authors.lastname: Zeng
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Raymond
authors.initials: R
authors.lastname: Laflamme