Shadow tomography based on informationally complete positive operator-valued measure

Atithi Acharya, Siddhartha Saha, and Anirvan M. Sengupta
Phys. Rev. A 104, 052418 – Published 16 November 2021

Abstract

Recently introduced shadow tomography protocols use “classical shadows” of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate recovery of the density matrix for high rank mixed states. Yet, such a protocol makes multiple accurate predictions with high confidence, based on a moderate number of quantum measurements. One particular influential algorithm, proposed by Huang et al. [Huang, Kueng, and Preskill, Nat. Phys. 16, 1050 (2020)], requires additional circuits for performing certain random unitary transformations. In this paper, we avoid these transformations but employ an arbitrary informationally complete positive operator-valued measure and show that such a procedure can compute k-bit correlation functions for quantum states reliably. We also show that, for this application, we do not need the median of means procedure of Huang et al. Finally, we discuss the contrast between the computation of correlation functions and fidelity of reconstruction of low rank density matrices.

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  • Received 3 June 2021
  • Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevA.104.052418

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Atithi Acharya1, Siddhartha Saha1, and Anirvan M. Sengupta1,2

  • 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 2Center for Computational Mathematics and Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA

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Issue

Vol. 104, Iss. 5 — November 2021

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