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Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables

  • Lu, D
  • Xin, T
  • Yu, N
  • Ji, Z
  • Chen, J
  • Long, G
  • Baugh, J
  • Peng, X
  • Zeng, B
  • Laflamme, R
Publication Date
Jun 07, 2016
UTS Institutional Repository


© 2016 American Physical Society. 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.

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