تقرير
Coherent information for CSS codes under decoherence
| العنوان: | Coherent information for CSS codes under decoherence |
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| المؤلفون: | Niwa, Ryotaro, Lee, Jong Yeon |
| سنة النشر: | 2024 |
| المجموعة: | Condensed Matter Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Condensed Matter - Statistical Mechanics |
| الوصف: | Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood (ML) decoder always succeeds in the asymptotic limit. Thus, the fundamental threshold is saturated by the optimal decoder. Comment: 11+3 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2407.02564Test |
| رقم الانضمام: | edsarx.2407.02564 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |