Kliesch, M., Kueng, R., Eisert, J. and Gross, D. (2019). Guaranteed recovery of quantum processes from few measurements. Quantum, 3. WIEN: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF. ISSN 2521-327X

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Abstract

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.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Kliesch, M.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kueng, R.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Eisert, J.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Gross, D.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-144641
Journal or Publication Title: Quantum
Volume: 3
Date: 2019
Publisher: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
Place of Publication: WIEN
ISSN: 2521-327X
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
INEQUALITIES; SIMULATIONS; DIAMOND; SIGNAL; NORMMultiple languages
Quantum Science & Technology; Physics, MultidisciplinaryMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/14464

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