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Almost Qudits in the Prepare-and-Measure Scenario
Jef Pauwels1, Stefano Pironio1, Erik Woodhead1
1Laboratoire d'Information Quantique, CP 225, Université libre de Bruxelles (ULB), Avenue F. D. Roosevelt 50, 1050 Bruxelles, Belgium.
Physical Review Letters
|January 6, 2023
Summary
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.
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.
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