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Paper 1
Quantum soundness of testing tensor codes
Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, Henry Yuen
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2111.08131
- arXiv
- 2111.08131
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.
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