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arXiv · 2609.36273

Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes

Nicolai Peder Bülow Pedersen·Jakob Kaltoft Søndergaard·Jaron Skovsted Gundersen·René Bødker Christensen·Petar Popovski
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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.

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Nicolai Peder Bülow Pedersen, Jakob Kaltoft Søndergaard, Jaron Skovsted Gundersen, René Bødker Christensen, Petar Popovski. 2026-09-28. Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes. https://arxiv.org/abs/2609.36273

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