Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes
Abstract
Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.
Related
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BibTeX
@misc{pedersen2026puncturing,
title = {{Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes}},
author = {Nicolai Peder Bülow Pedersen and Jakob Kaltoft Søndergaard and Jaron Skovsted Gundersen and René Bødker Christensen and Petar Popovski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36273},
eprint = {2609.36273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36273},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes
AU - Nicolai Peder Bülow Pedersen
AU - Jakob Kaltoft Søndergaard
AU - Jaron Skovsted Gundersen
AU - René Bødker Christensen
AU - Petar Popovski
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36273
UR - https://arxiv.org/abs/2609.36273
AB - Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.
ER -