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Guaranteed recovery of quantum processes from few measurements

Citation Link: https://doi.org/10.15480/882.14044
Publikationstyp
Journal Article
Date Issued
2019-08-12
Sprache
English
Author(s)
Kliesch, Martin  
Kueng, Richard  
Eisert, Jens  
Gross, David  
TORE-DOI
10.15480/882.14044
TORE-URI
http://hdl.handle.net/11420/13933
Journal
Quantum  
Volume
3
Start Page
171
Citation
Quantum 3: 171 (2019-08-12)
Publisher DOI
10.22331/q-2019-08-12-171
Scopus ID
2-s2.0-85094915618
ArXiv ID
1701.03135v4
Publisher
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case. Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and `2-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.
DDC Class
530: Physik
Lizenz
https://creativecommons.org/licenses/by/4.0/
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