Compressed-sensing tomography for qudits in Hilbert spaces of non-power-of-two dimensions

Revanth Badveli, Vinayak Jagadish, R. Srikanth, and Francesco Petruccione
Phys. Rev. A 101, 062328 – Published 22 June 2020

Abstract

The techniques of low-rank matrix recovery were adapted for quantum state tomography (QST) previously by Gross et al. [Phys. Rev. Lett. 105, 150401 (2010)] where they consider the tomography of n spin-1/2 systems. For the density matrix of dimension d=2n and rank r with r2n, it was shown that randomly chosen Pauli measurements of the order O[drlog(d)2] are enough to fully reconstruct the density matrix by running a specific convex optimization algorithm. The result utilized the low operator norm of the Pauli operator basis, which makes it “incoherent” to low-rank matrices. For quantum systems of dimension d not a power of two, Pauli measurements are not available, and one may consider using SU(d) measurements. Here, we point out that the SU(d) operators, owing to their high operator norm, do not provide a significant savings in the number of measurement settings required for successful recovery of all rank-r states. We propose an alternative strategy in which the quantum information is swapped into the subspace of a power-two system using only poly[log(d)2] gates at most with QST being implemented, subsequently, by performing O[drlog(d)2] Pauli measurements. We show that, despite the increased dimensionality, this method is more efficient than the one using SU(d) measurements.

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  • Received 9 March 2020
  • Accepted 1 June 2020

DOI:https://doi.org/10.1103/PhysRevA.101.062328

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Quantum Information, Science & Technology

Authors & Affiliations

Revanth Badveli1,2,*, Vinayak Jagadish2,3,†, R. Srikanth4, and Francesco Petruccione2,3

  • 1Computer Science and Information Systems, BITS Pilani-Goa Campus, Goa 403 726, India
  • 2Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa
  • 3National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, Durban 4001, South Africa
  • 4Poornaprajna Institute of Scientific Research, Bangalore 560 080, India

  • *badveli.revanth@gmail.com
  • jagadishv@ukzn.ac.za

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Issue

Vol. 101, Iss. 6 — June 2020

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