Canonical forms of two-qubit states under local operations

Sudha, H. S. Karthik, Rajarshi Pal, K. S. Akhilesh, Sibasish Ghosh, K. S. Mallesh, and A. R. Usha Devi
Phys. Rev. A 102, 052419 – Published 23 November 2020

Abstract

Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding nonlocality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown [Phys. Rev. A 64, 010101(R) (2001)] that an arbitrary two-qubit state gets transformed under SLOCC into one of the two different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other a nondiagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et al. [Phys. Rev. A 64, 010101(R) (2001)] required highly nontrivial results on matrix decompositions in n-dimensional spaces with an indefinite metric. Here we employ an entirely different approach—inspired by the methods developed by Rao et al. [J. Mod. Opt. 45, 955 (1998)] in classical polarization optics—which leads naturally towards the identification of two inequivalent SLOCC invariant canonical forms for two-qubit states. In addition, our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.

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  • Received 6 July 2020
  • Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.052419

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Sudha1,2, H. S. Karthik3, Rajarshi Pal4, K. S. Akhilesh5, Sibasish Ghosh6, K. S. Mallesh5,7, and A. R. Usha Devi8,2,*

  • 1Department of Physics, Kuvempu University, Shankaraghatta-577 451, Karnataka, India
  • 2Inspire Institute, Inc., Alexandria, Virginia, 22303, USA
  • 3International Centre for Theory of Quantum Technologies, University of Gdańsk, Gdańsk 80-308, Poland
  • 4Department of Physics, Sungkyunkwan University, Suwon 16419, Korea
  • 5Department of Studies in Physics, University of Mysore, Manasagangotri, Mysuru 570006, Karnataka, India
  • 6Optics & Quantum Information Group, The Institute of Mathematical Sciences, HBNI,C. I. T. Campus, Taramani, Chennai 600113, India
  • 7Regional Institute of Education (NCERT), Mysuru 570006, India
  • 8Department of Physics, Bangalore University, Bangalore 560 056, India

  • *arutth@rediffmail.com

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Issue

Vol. 102, Iss. 5 — November 2020

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