Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds

Details Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds

2002-11-27

arxiv.org/abs/quant-ph/0211179v1

Physics

Quantum Physics

10 pages, no figures

Scientific paper

We show that an oracle A that contains either 1/4 or 3/4 of all strings of length n can be used to separate EQP from the counting classes MOD_{p^k}P. Our proof makes use of the degree of a representing polynomial over the finite field of size p^k. We show a linear lower bound on the degree of this polynomial. We also show an upper bound of O(n^{1/log_p m}) on the degree over the ring of integers modulo m, whenever m is a squarefree composite with largest prime factor p.

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