Adaptive compressive tomography: A numerical study

Ahn D, Teo YS, Jeong H, Koutny D, Rehacek J, Hradil Z, Leuchs G, Sanchez-Soto LL (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Physical Review A American Physical Society

Book Volume: 100

Article Number: 012346

Journal Issue: 1

DOI: 10.1103/PhysRevA.100.012346

Abstract

We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al., Phys. Rev. Lett. 122, 100404 (2019)10.1103/PhysRevLett.122.100404], which significantly reduces the number of measurement settings to unambiguously reconstruct any rank-deficient state without any a priori knowledge besides its dimension. We show that both entangled and product bases chosen by our adaptive scheme perform comparably well with recently known compressed-sensing element-probing measurements, and also beat random measurement bases for low-rank quantum states. We also numerically conjecture asymptotic scaling behaviors for this number as a function of the state rank for our adaptive schemes. These scaling formulas appear to be independent of the Hilbert-space dimension. As a natural development, we establish a faster hybrid compressive scheme that first chooses random bases, and later adaptive bases as the scheme progresses. As an epilogue, we reiterate important elements of informational completeness for our adaptive scheme.

Authors with CRIS profile

Gerhard Leuchs

Involved external institutions

Max-Planck-Institut für die Physik des Lichts (MPL) / Max Planck Institute for the Science of Light DE Germany (DE) Palacky University Olomouc / Univerzita Palackého v Olomouci CZ Czech Republic (CZ) Seoul National University (SNU) / 서울대학교 KR Korea, Republic of (KR)

How to cite

APA:

Ahn, D., Teo, Y.S., Jeong, H., Koutny, D., Rehacek, J., Hradil, Z.,... Sanchez-Soto, L.L. (2019). Adaptive compressive tomography: A numerical study. Physical Review A, 100(1). https://doi.org/10.1103/PhysRevA.100.012346

MLA:

Ahn, D., et al. "Adaptive compressive tomography: A numerical study." Physical Review A 100.1 (2019).

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