Conclusive exclusion of quantum states

Somshubhro Bandyopadhyay, Rahul Jain, Jonathan Oppenheim, and Christopher Perry
Phys. Rev. A 89, 022336 – Published 25 February 2014

Abstract

In the task of quantum state exclusion, we consider a quantum system prepared in a state chosen from a known set. The aim is to perform a measurement on the system which can conclusively rule that a subset of the possible preparation procedures cannot have taken place. We ask what conditions the set of states must obey in order for this to be possible and how well we can complete the task when it is not. The task of quantum state discrimination forms a subclass of this set of problems. Within this paper, we formulate the general problem as a semidefinite program (SDP), enabling us to derive sufficient and necessary conditions for a measurement to be optimal. Furthermore, we obtain a necessary condition on the set of states for exclusion to be achievable with certainty, and we give a construction for a lower bound on the probability of error. This task of conclusively excluding states has gained importance in the context of the foundations of quantum mechanics due to a result from Pusey, Barrett, and Rudolph (PBR). Motivated by this, we use our SDP to derive a bound on how well a class of hidden variable models can perform at a particular task, proving an analog of Tsirelson's bound for the PBR experiment and the optimality of a measurement given by PBR in the process. We also introduce variations of conclusive exclusion, including unambiguous state exclusion, and state exclusion with worst-case error.

  • Received 21 June 2013
  • Corrected 15 July 2014

DOI:https://doi.org/10.1103/PhysRevA.89.022336

©2014 American Physical Society

Corrections

15 July 2014

Erratum

Publisher's Note: Conclusive exclusion of quantum states [Phys. Rev. A 89, 022336 (2014)]

Somshubhro Bandyopadhyay, Rahul Jain, Jonathan Oppenheim, and Christopher Perry
Phys. Rev. A 90, 019902 (2014)

Authors & Affiliations

Somshubhro Bandyopadhyay1, Rahul Jain2, Jonathan Oppenheim2,3, and Christopher Perry3,*

  • 1Department of Physics and Center for Astroparticle Physics and Space Science, Bose Institute, Block EN, Sector V, Bidhan Nagar, Kolkata 700091, India
  • 2Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615
  • 3Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

  • *Corresponding author: christopher.perry.12@ucl.ac.uk

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Issue

Vol. 89, Iss. 2 — February 2014

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