Hiding instances in multioracle queries
STACS 90 Proceedings of the seventh annual symposium on Theoretical aspects of computer science
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Highly resilient correctors for polynomials
Information Processing Letters
Random-self-reducibility of complete sets
SIAM Journal on Computing
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
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Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Interaction in quantum communication and the complexity of set disjointness
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Breaking the O(n1/(2k-1)) Barrier for Information-Theoretic Private Information Retrieval
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Upper Bound on Communication Complexity of Private Information Retrieval
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Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum Oracle Interrogation: Getting All Information for Almost Half the Price
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The quantum complexity of set membership
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Better Lower Bounds for Locally Decodable Codes
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
New bounds in secret-key agreement: the gap between formation and secrecy extraction
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
IEEE Transactions on Information Theory - Part 1
Limits on the ability of quantum states to convey classical messages
Journal of the ACM (JACM)
A tight lower bound for restricted PIR protocols
Computational Complexity
Towards 3-query locally decodable codes of subexponential length
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Towards 3-query locally decodable codes of subexponential length
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Lower bounds for predecessor searching in the cell probe model
Journal of Computer and System Sciences
The Complexity of Local List Decoding
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ACM Transactions on Computation Theory (TOCT)
Communications of the ACM
Two-query PCP with subconstant error
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Quantum private queries: security analysis
IEEE Transactions on Information Theory
Postselection finite quantum automata
UC'10 Proceedings of the 9th international conference on Unconventional computation
Relativized worlds without worst-case to average-case reductions for NP
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SIAM Journal on Computing
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantum predictive learning and communication complexity with single input
Quantum Information & Computation
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
ACM Transactions on Computation Theory (TOCT)
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
New bounds for matching vector families
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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A locally decodable code (LDC) encodes n-bit strings x in m-bit codewords C(x) in such a way that one can recover any bit xi from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2 classical queries require exponential length: m = 2Ω(n). Previously, this was known only for linear codes (Goldreich et al., in: Proceedings of 17th IEEE Conference on Computation Complexity, 2002, pp. 175-183). The proof proceeds by showing that a 2-query LDC can be decoded with a single quantum query, when defined in an appropriate sense. It goes on to establish an exponential lower bound on any 'l-query locally quantum-decodable code'. We extend our lower bounds to non-binary alphabets and also somewhat improve the polynomial lower bounds by Katz and Trevisan for LDCs with more than 2 queries. Furthermore, we show that q quantum queries allow more succinct LDCs than the best known LDCs with q classical queries. Finally, we give new classical lower bounds and quantum upper bounds for the setting of private information retrieval. In particular, we exhibit a quantum 2-server private information retrieval (PIR) scheme with O(n3/10) qubits of communication, beating the O(n1/3) bits of communication of the best known classical 2-server PIR.