title: Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables.
abstract: Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.
authors.forename: Dawei
authors.initials: D
authors.lastname: Lu
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.|State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Xin
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.|Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007, Australia.|Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada.
authors.forename: Nengkun
authors.initials: N
authors.lastname: Yu
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.|State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, 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 20742, USA.
authors.forename: Jianxin
authors.initials: J
authors.lastname: Chen
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 N2L 3G1, Ontario, Canada.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Baugh
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, China.
authors.forename: Xinhua
authors.initials: X
authors.lastname: Peng
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.|Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada.|Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada.
authors.forename: Bei
authors.initials: B
authors.lastname: Zeng
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.|Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Raymond
authors.initials: R
authors.lastname: Laflamme