Optimizing Shadow Tomography with Generalized Measurements

H. Chau Nguyen, Jan Lennart Bönsel, Jonathan Steinberg, and Otfried Gühne
Phys. Rev. Lett. 129, 220502 – Published 23 November 2022
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Abstract

Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system. Traditional tomography is limited to a handful of qubits, and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analyzed based on outcomes of ideal projective measurements on the system upon application of randomized unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalized measurements, or positive operator valued measures. Based on the idea of the least-square estimator shadow tomography with generalized measurements is both more general and simpler than the traditional formulation with randomization of unitaries. In particular, this formulation allows us to analyze theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Moreover, with this generalization we also demonstrate how the optimization of measurements for shadow tomography tailored toward a particular set of observables can be carried out.

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  • Received 20 June 2022
  • Revised 27 October 2022
  • Accepted 31 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.220502

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

H. Chau Nguyen*, Jan Lennart Bönsel, Jonathan Steinberg, and Otfried Gühne§

  • Naturwissenschaftlich–Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany

  • *chau.nguyen@uni-siegen.de
  • jan.boensel@uni-siegen.de
  • steinberg@physik.uni-siegen.de
  • §otfried.guehne@uni-siegen.de

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Issue

Vol. 129, Iss. 22 — 23 November 2022

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