ECCC-Report TR11-040https://eccc.weizmann.ac.il/report/2011/040Comments and Revisions published for TR11-040en-usTue, 22 Mar 2011 21:42:41 +0200
Paper TR11-040
| Strong Direct Product Theorems for Quantum Communication and Query Complexity |
Alexander A. Sherstov
https://eccc.weizmann.ac.il/report/2011/040A strong direct product theorem (SDPT) states that solving $n$ instances of a problem requires $\Omega(n)$ times the resources for a single instance, even to achieve success probability $2^{-\Omega(n)}.$ We prove that quantum communication complexity obeys an SDPT whenever the communication lower bound for a single instance is proved by the generalized discrepancy method, the strongest technique in that model. We prove that quantum query complexity obeys an SDPT whenever the query lower bound for a single instance is proved by the polynomial method, one of the two main techniques in that model. In both models, we prove the corresponding XOR lemmas and threshold direct product theorems.
Tue, 22 Mar 2011 21:42:41 +0200https://eccc.weizmann.ac.il/report/2011/040