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  • Letter
  • Open Access

Operational interpretation of the Choi rank through exclusion tasks

Benjamin Stratton1,2,*, Chung-Yun Hsieh2, and Paul Skrzypczyk2,3

  • 1Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol, Bristol BS8 1FD, United Kingdom
  • 2H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
  • 3CIFAR Azrieli Global Scholars Program, CIFAR, Toronto, Canada

  • *Contact author: ben.stratton@bristol.ac.uk
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Phys. Rev. A 110, L050601 – Published 13 November, 2024

DOI: https://doi.org/10.1103/PhysRevA.110.L050601

Abstract

The Choi state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi state can greatly simplify problems. It also offers an alternative approach to the characterization of a channel, with properties of the Choi state providing novel insight into a channel's behavior. The rank of a Choi state, termed the Choi rank, has proven to be an important characterizing property, and here, its significance is further elucidated through an operational interpretation. The Choi rank is shown to provide a universal bound on how successfully two agents, Alice and Bob, can perform an entanglement-assisted exclusion task. The task can be considered an extension of superdense coding, where Bob can only output information about Alice's encoded bit string with certainty. Conclusive state exclusion, in place of state discrimination, is therefore considered at the culmination of the superdense coding protocol. In order to prove this result, a necessary condition for conclusive k-state exclusion of a set of states is presented in order to achieve this result, and the notions of weak and strong exclusion are introduced.

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Corrections

4 May, 2026

Correction: A typographical error in the EPSRC UK grant number contained an error and has been fixed.

Article Text

Supplemental Material

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Outline

Information

Phys. Rev. A 110, L050601– Published 13 November, 2024
  • Received 17 June 2024
  • Revised 16 September 2024
  • Accepted 21 October 2024
  • Corrected 4 May 2026
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