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Almost Qudits in the Prepare-and-Measure Scenario.

Jef Pauwels1, Stefano Pironio1, Erik Woodhead1

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This study explores quantum information in systems that are almost, but not exactly, standard qudits. Findings show these systems can compromise quantum protocols, but a new method helps analyze and secure them.

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Area of Science:

  • Quantum Information Science
  • Quantum Communication Protocols
  • Quantum Computing Theory

Background:

  • Quantum communication research often assumes precise Hilbert space dimensions.
  • Real-world quantum systems may approximate standard dimensions (qudits) but possess higher-dimensional characteristics.
  • This approximation can impact the security and validity of quantum information protocols.

Purpose of the Study:

  • To introduce and investigate quantum information encoded in "almost qudit" systems.
  • To demonstrate the vulnerability of semi-device-independent quantum information protocols to these systems.
  • To develop a robust method for analyzing and securing quantum correlations in such scenarios.

Main Methods:

  • Introduction of "almost qudit" systems for quantum information encoding.
  • Analysis of the impact of these systems on semi-device-independent protocols.
  • Development of a general method using semidefinite relaxations to bound almost qudit correlations.
  • Application of the method to device-independent tests of quantum dimensions.
  • Investigation of almost qubit systems as a resource for random access codes.

Main Results:

  • Small higher-dimensional components in almost qudit systems can significantly compromise established quantum information protocols.
  • A general method based on semidefinite relaxations is provided for bounding almost qudit correlations.
  • The developed method offers a systematic approach for device-independent tests of classical and quantum dimensions.
  • Optimal quantum protocols for random access codes using almost qubit systems were determined.

Conclusions:

  • Almost qudit systems pose a significant challenge to the security and reliability of quantum communication protocols.
  • Semidefinite relaxations provide a powerful tool for analyzing and mitigating the risks associated with these systems.
  • The findings contribute to more robust device-independent quantum information processing and resource optimization.