Work

Geometrical Constructions of Purity Testing Protocols and Their Applications to Quantum Communication

Year: 2026

Type: article

Abstract: Purity testing protocols (PTPs), also known as Bell state testing protocols, i.e., protocols that decide with high probability whether or not a distributed bipartite quantum state is a tensor product of Bell states, have been proven to be a useful tool in many quantum communication applications. In this paper, we provide geometrical constructions for such protocols that originate directly from classical linear error correcting codes (LECCs), in a way that the properties of the resulting PTP are completely determined from those of the LECC used in the construction. We investigate the implications of our results in various quantum communication tasks, including error detection, entanglement purification for general quantum error models and quantum message authentication.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2026.3678348

Authors: Róbert Trényi, Simeon Ball, David G. Glynn, Marcos Curty

Institutions: University of the Basque Country, Universitat Politècnica de Catalunya, Flinders University, Universidade de Vigo

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,645

Funders: European Commission, Eusko Jaurlaritza, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap