Pearson correlation coefficient as a measure for certifying and quantifying high-dimensional entanglement

C. Jebarathinam, Dipankar Home, and Urbasi Sinha
Phys. Rev. A 101, 022112 – Published 24 February 2020

Abstract

A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of this scheme for the high-dimensional states, a key step has been taken in a very recent work by experimentally determining PCC and analytically relating it to Negativity for quantifying entanglement of the empirically produced bipartite pure state of spatially correlated photonic qutrits. Motivated by this work, we present here a comprehensive study of the efficacy of such an entanglement characterizing scheme for a range of bipartite qutrit states by considering suitable combinations of PCCs based on a limited number of measurements. For this purpose, we investigate the issue of necessary and sufficient certification together with quantification of entanglement for the two-qutrit states comprising maximally entangled state mixed with white noise and colored noise in two different forms, respectively. Further, by considering these classes of states for d=4 and 5, extension of this PCC-based approach for higher dimensions (d) is discussed.

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  • Received 10 September 2019
  • Accepted 28 January 2020

DOI:https://doi.org/10.1103/PhysRevA.101.022112

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

C. Jebarathinam1,*, Dipankar Home2, and Urbasi Sinha3,†

  • 1S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 106, India
  • 2Bose Institute, Centre for Astroparticle Physics and Space Science (CAPSS), Block EN, Sector V, Salt Lake, Kolkata 700 091, India
  • 3Light and Matter Physics, Raman Research Institute, Bengaluru-560080, India

  • *Present address: Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan.
  • usinha@rri.res.in

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Issue

Vol. 101, Iss. 2 — February 2020

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