A New Quantum Lower Bound Method, with an Application to a Strong Direct Product Theorem for Quantum Search

Abstract: We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product theorem for quantum search. This result was previously proved by Klauck, Spalek, and de Wolf (FOCS'04) using the polynomials method. No proof using the adversary method was known before.

• Type: Journal
• Year: 2010
• Where: TOC
• Authors: Andris Ambainis
• Keywords: Adversary Method, Direct Product Theorem, Management, Polynomials Method, TOC 2010