New perspectives on covariant quantum error correction
- URL: http://arxiv.org/abs/2005.11918v3
- Date: Sun, 1 Aug 2021 00:36:54 GMT
- Title: New perspectives on covariant quantum error correction
- Authors: Sisi Zhou, Zi-Wen Liu and Liang Jiang
- Abstract summary: We prove new and powerful lower bounds on the infidelity of covariant quantum error correction.
Explicit lower bounds are derived for both erasure and depolarizing noises.
We also present a type of covariant codes which nearly saturates these lower bounds.
- Score: 3.3811802886738462
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Covariant codes are quantum codes such that a symmetry transformation on the
logical system could be realized by a symmetry transformation on the physical
system, usually with limited capability of performing quantum error correction
(an important case being the Eastin--Knill theorem). The need for understanding
the limits of covariant quantum error correction arises in various realms of
physics including fault-tolerant quantum computation, condensed matter physics
and quantum gravity. Here, we explore covariant quantum error correction with
respect to continuous symmetries from the perspectives of quantum metrology and
quantum resource theory, establishing solid connections between these formerly
disparate fields. We prove new and powerful lower bounds on the infidelity of
covariant quantum error correction, which not only extend the scope of previous
no-go results but also provide a substantial improvement over existing bounds.
Explicit lower bounds are derived for both erasure and depolarizing noises. We
also present a type of covariant codes which nearly saturates these lower
bounds.
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