Measure of not-completely-positive qubit maps: The general case

Vinayak Jagadish, R. Srikanth, and Francesco Petruccione
Phys. Rev. A 100, 012336 – Published 23 July 2019

Abstract

We show that the set of not-completely-positive (NCP) maps is unbounded, unless further assumptions are made. This is done by first proposing a reasonable definition of a valid NCP map, which is nontrivial because NCP maps may lack a full positivity domain. The definition is motivated by specific examples. We prove that for valid NCP maps, the eigenvalue spectrum of the corresponding dynamical matrix is not bounded. Based on this, we argue that in general the volume measure of qubit maps, including NCP maps, is not well defined.

  • Figure
  • Received 2 April 2019

DOI:https://doi.org/10.1103/PhysRevA.100.012336

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Vinayak Jagadish1,2,*, R. Srikanth3,†, and Francesco Petruccione1,2,‡

  • 1Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa
  • 2National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa
  • 3Poornaprajna Institute of Scientific Research, Bangalore 560 080, India

  • *jagadishv@ukzn.ac.za
  • srik@poornaprajna.org
  • petruccione@ukzn.ac.za

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Issue

Vol. 100, Iss. 1 — July 2019

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