Compressively Certifying Quantum Measurements

Year: 2020

Authors: Gianani I., Teo YS., Cimini V., Jeong H., Leuchs G., Barbieri M., Sanchez-Soto LL.

Autors Affiliation: Univ Roma Tre, Dipartimento Sci, I-00146 Rome, Italy; Seoul Natl Univ, Dept Phys & Astron, Seoul 08826, South Korea; Max Planck Inst Phys Lichts, Staudtstr 2, D-91058 Erlangen, Germany; Russian Acad Sci, Inst Appl Phys, Nizhnii Novgorod 603950, Russia; CNR, Ist Nazl Ott, Largo Enrico Fermi 2, I-50125 Florence, Italy; Univ Complutense, Fac Fis, Dept Opt, Madrid 28040, Spain.

Abstract: We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is most compressive when the measurement constitutes pure detection outcomes, requiring only an informationally complete number of probe states that scales linearly with the system dimension. We argue and provide numerical evidence showing that the minimal number of probe states needed is even generally below the numbers known in the closely related classical phase-retrieval problem because of the quantum constraint. We also present affirmative results with polarization experiments that illustrate significant compressive behaviors for both two- and four-qubit detectors just by using random product probe states.

Journal/Review: PRX QUANTUM

Volume: 1 (2)      Pages from: 20307-1  to: 20307-11

More Information: We thank Emanuele Roccia for useful discussion. This work is supported in part by the National Research Foundation of Korea (NRF) (Grant Nos. NRF2019R1A6A1A10073437, No. NRF-2019M3E4A108 0074, and No. NRF-2020R1A2C1008609), the Spanish MINECO (Grant Nos. FIS201567963-P and No. PGC2018-099183-B-I00), European Union’s Horizon 2020 research and innovation program (Project QuantERA ApresSF), and a Mega-grant of the Ministry of Education and Science of the Russian Federation (Contract No.14.W03.31.0032). I.G. is supported by Ministero dell’Istruzione, dell’Universita e della Ricerca Grant of Excellence Departments (ARTICOLO 1, COMMI 314337 LEGGE 232/2016).
KeyWords: Tomography
DOI: 10.1103/PRXQuantum.1.020307

Citations: 10
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