دسته بندی:
محاسبات کوانتومی - Quantum-Computing
سال انتشار:
2022
عنوان انگلیسی مقاله:
Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes
ترجمه فارسی عنوان مقاله:
اثبات های آنتروپیک کرانه های سینگلتون برای کدهای تصحیح خطای کوانتومی
منبع:
ieee - ieee Transactions on Information Theory;2022;68;6;10:1109/TIT:2022:3149291
نویسنده:
Markus Grassl; Felix Huber; Andreas Winter
چکیده انگلیسی:
We show that a relatively simple reasoning using
von Neumann entropy inequalities yields a robust proof of the
quantum Singleton bound for quantum error-correcting codes
(QECC). For entanglement-assisted quantum error-correcting
codes (EAQECC) and catalytic codes (CQECC), a type of
generalized quantum Singleton bound [Brun et al., IEEE Trans.
Inf. Theory 60(6):3073–3089 (2014)] was believed to hold for
many years until recently one of us found a counterexample
[MG, Phys. Rev. A 103, 020601 (2021)]. Here, we rectify this state
of affairs by proving the correct generalized quantum Singleton
bound, extending the above-mentioned proof method for QECC;
we also prove information-theoretically tight bounds on the
entanglement-communication tradeoff for EAQECC. All of the
bounds relate block length n and code length k for given
minimum distance d and we show that they are robust, in the
sense that they hold with small perturbations for codes which
only correct most of the erasure errors of less than d letters.
In contrast to the classical case, the bounds take on qualitatively
different forms depending on whether the minimum distance
is smaller or larger than half the block length. We also provide a propagation rule: any pure QECC yields an EAQECC
with the same distance and dimension, but of shorter block
length.
Index Terms: Quantum codes | quantum entanglement | singleton bound.
قیمت: رایگان
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