Ultimate precision of direct tomography of wave functions

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 i...

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Bibliographic Details
Published in:Quantum information processing 2021-07, Vol.20 (7), Article 221
Main Authors: Nguyen, Xuan-Hoai Thi, Choi, Mahn-Soo
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Tomography
Wave functions
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03167-0