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.
Bibliographical notePublisher Copyright:
© 2021, The Author(s).
- Heisenberg limit
- Quantum metrology
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