Ultimate precision of direct tomography of wave functions

Xuan Hoai Thi Nguyen, Mahn Soo Choi

Research output: Contribution to journalArticlepeer-review


In contrast to the standard quantum state tomography, the direct tomography seeks a direct access to the complex values of the wave function at particular positions. Originally put forward as a special case of weak measurement, it has been extended to arbitrary measurement setup. We generalize the idea of “quantum metrology,” where a real-valued phase is estimated, to the estimation of complex-valued phase. We show that it enables to identify the optimal measurements and investigate the fundamental precision limit of the direct tomography. We propose a few experimentally feasible examples of direct tomography schemes and, based on the complex phase estimation formalism, demonstrate that direct tomography can reach the Heisenberg limit.

Original languageEnglish
Article number221
JournalQuantum Information Processing
Issue number7
Publication statusPublished - 2021 Jul

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).


  • Heisenberg limit
  • Quantum metrology
  • Tomography

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering


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