Quantum soundness of testing tensor codes
Abstract
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.
Keywords
Cite
@article{arxiv.2111.08131,
title = {Quantum soundness of testing tensor codes},
author = {Zhengfeng Ji and Anand Natarajan and Thomas Vidick and John Wright and Henry Yuen},
journal= {arXiv preprint arXiv:2111.08131},
year = {2022}
}
Comments
v3: published version