Quantum Soundness of Testing Tensor Codes
- Publication Type:
- Journal Article
- Citation:
- Discrete Analysis, 2022, 2022
- Issue Date:
- 2022-01-01
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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 generalizes to the infinite-dimensional commuting-operator model of quantum provers.
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