The Multiplicative Quantum Adversary

We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants upper-bound the difference of the progress function, whereas our new variant upper-bounds the ratio and that is why we coin it the multiplicative adversary. Our new method generalizes the quantum lower-bound method by Ambainis [Amb05, ASW06], based on the analysis of eigenspaces of the density matrix, to all functions. We prove a strong direct product theorem for all functions that have a multiplicative adversary lower bound.

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Robert Spalek
• Keywords: Adversary Methods, Algorithms, COCO 2008, Multiplicative Adversary, Quantum Adversary Method