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Peer-reviewedCC BY 4.0New Journal of Physics

Self-testing of logical subspaces of quantum error-correcting codes

  • Li-Yi Hsu1,2
  • En-Jui Kuo3
  1. 1Chung Yuan Christian University
  2. 2National Center for Theoretical Sciences
  3. 3National Yang Ming Chiao Tung University
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Abstract

We develop explicit device-independent self-testing constructions for logical subspaces of quantum error-correcting codes. By constructing multipartite Bell inequalities tailored to stabilizer code structures, we show that maximal quantum violations uniquely certify that the underlying shared state resides within the logical subspace of a given code, up to local isometries. These constructions extend earlier stabilizer-subspace self-testing results beyond the five-qubit code to several representative stabilizer codes, including the six-qubit code, the Steane code, and Shor’s nine-qubit code. The tilted sum-of-squares variants further impose algebraic constraints on the relative weights of the logical sectors. Together, these results provide explicit examples of device-independent self-testing for representative stabilizer-code logical subspaces and suggest possible directions for verification and benchmarking of encoded quantum information.

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Cite

BibTeXRIS
BibTeX
@article{hsu2026selftesting,
  title = {{Self-testing of logical subspaces of quantum error-correcting codes}},
  author = {Li-Yi Hsu and En-Jui Kuo},
  journal = {New Journal of Physics},
  year = {2026},
  month = oct,
  doi = {10.1088/1367-2630/aeb3a3},
  url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeb3a3},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Self-testing of logical subspaces of quantum error-correcting codes
AU  - Li-Yi Hsu
AU  - En-Jui Kuo
PY  - 2026
DA  - 2026/10/23
JO  - New Journal of Physics
DO  - 10.1088/1367-2630/aeb3a3
UR  - https://iopscience.iop.org/article/10.1088/1367-2630/aeb3a3
AB  - We develop explicit device-independent self-testing constructions for logical subspaces of quantum error-correcting codes. By constructing multipartite Bell inequalities tailored to stabilizer code structures, we show that maximal quantum violations uniquely certify that the underlying shared state resides within the logical subspace of a given code, up to local isometries. These constructions extend earlier stabilizer-subspace self-testing results beyond the five-qubit code to several representative stabilizer codes, including the six-qubit code, the Steane code, and Shor’s nine-qubit code. The tilted sum-of-squares variants further impose algebraic constraints on the relative weights of the logical sectors. Together, these results provide explicit examples of device-independent self-testing for representative stabilizer-code logical subspaces and suggest possible directions for verification and benchmarking of encoded quantum information.
SN  - 1367-2630
ER  -