Geodesic
Quantum soundness of testing tensor codes
Discrete analysis (2022) Cet article a éte moissonné depuis la source Scholastica

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A locally testable code is an error-correcting code that admits very efficient probabilistic tests of membership. Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of Reed-Muller codes. The natural test for tensor codes, the axis-parallel line vs. point test, plays an essential role in constructions of probabilistically checkable proofs. We analyze the axis-parallel line vs. point test as a two-prover game and show that the test is sound against quantum provers sharing entanglement. Our result implies the quantum-soundness of the low individual degree test, which is an essential component of the MIP* = RE theorem. Our proof also generalizes to the infinite-dimensional commuting-operator model of quantum provers.
Publié le : 
@article{DAS_2022_a3,
     author = {Zhengfeng Ji and Anand Natarajan and Thomas Vidick and John Wright and Henry Yuen},
     title = {Quantum soundness of testing tensor codes},
     journal = {Discrete analysis},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2022_a3/}
}
TY  - JOUR
AU  - Zhengfeng Ji
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AU  - Thomas Vidick
AU  - John Wright
AU  - Henry Yuen
TI  - Quantum soundness of testing tensor codes
JO  - Discrete analysis
PY  - 2022
UR  - http://geodesic.mathdoc.fr/item/DAS_2022_a3/
LA  - en
ID  - DAS_2022_a3
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%A Thomas Vidick
%A John Wright
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%J Discrete analysis
%D 2022
%U http://geodesic.mathdoc.fr/item/DAS_2022_a3/
%G en
%F DAS_2022_a3
Zhengfeng Ji; Anand Natarajan; Thomas Vidick; John Wright; Henry Yuen. Quantum soundness of testing tensor codes. Discrete analysis (2022). http://geodesic.mathdoc.fr/item/DAS_2022_a3/