We study the robust local testability of tensor products of two Algebraic-Geometry (AG) codes. In particular, we prove that \textit{constant rate} AG codes are robust locally testable. This significantly generalizes the seminal result of Polishchuk-Spielman [PS24], which proved robust local testability of Reed-Solomon codes. We establish an algebraic-geometric framework ... more >>>

Zero-knowledge codes, introduced by Decatur, Goldreich, and Ron (ePrint 1997), are error-correcting codes in which few codeword symbols reveal no information about the encoded message, and have been extensively used in cryptographic constructions. Quantum CSS codes, introduced by Calderbank and Shor (Phys. Rev. A 1996) and Steane (Royal Society A ... more >>>

The quantum analogue of the PCP theorem for QMA remains wide open. A central obstacle is the local indistinguishability of quantum codes: every sufficiently small view of an encoded witness is independent of the witness, seemingly preventing a local verifier from distinguishing YES from NO instances. One approach to this ... more >>>