Year: 2019
Type: article
Abstract: We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al., Phys. Rev. Lett. 122, 100404 (2019)], 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.
Source: Physical Review A
Authors: D. Ahn, Y. S. Teo, H. Jeong, D. Koutný, J. Řeháček, Z. Hradil, G. Leuchs, L. L. Sánchez-Soto
Institution: Seoul National University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: International Glaucoma Association, Grantová Agentura České Republiky, Ministry of Education, Ministry of Science, ICT and Future Planning, Univerzita Palackého v Olomouci, Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España, National Science Foundation, United Arab Emirates, European Research Council
OpenAlex ID: W2942905971