Teo, Yong SiahStruchalin, G. I.Kovlakov, E. V.Ahn, DaekunJeong, HyunseokStraupe, S. S.Kulik, S. P.Leuchs, GerdSánchez Soto, Luis Lorenzo2023-06-162023-06-162020-02-012469-992610.1103/PhysRevA.101.022334https://hdl.handle.net/20.500.14352/6114©2020 American Physical Society. We acknowledge financial support from the BK21 Plus Program (No. 21A20131111123) funded by the Ministry of Education (MOE, Korea) and National Research Foundation of Korea (NRF), the NRF grant funded by the Korea government (MSIP) (Grants No. NRF-2019M3E4A1080074, No. NRF-2019R1H1A3079890, and No. NRF-2018K2A9A1A06069933), Russian Foundation for Basic Research (RFBR Projects No. 19-32-80043 and No. 19-52-80034), Mega-grant of the Ministry of Education and Science of the Russian Federation (Contract No. 14.W03.31.0032), and the Spanish MINECO (Grants No. FIS2015-67963-P and No. PGC2018-099183-B-I00).We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely positive process with no spurious a priori information. It uses randomly chosen input states and adaptive output von Neumann measurements. Both entangled and tensor-product configurations are flexibly employable in our scheme, the latter of which are especially compatible with many-body quantum computing. Two main features of this scheme are the certification protocol that verifies whether the accumulated data uniquely characterize the quantum process and a compressive reconstruction method for the output states. We emulate multipartite scenarios with high-order transverse modes and optical fibers to demonstrate that, in terms of measurement resources, our assumption-free compressive strategy can reconstruct quantum processes almost equally efficiently using all types of input states and basis measurements.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.101.022334https://journals.aps.orgopen access535OpticsPhysicsAtomicMolecularChemicalÓptica (Física)2209.19 Óptica Física