TR04-120 Authors: Andris Ambainis, William Gasarch, Aravind Srinivasan, Andrey Utis

Publication: 21st December 2004 16:25

Downloads: 2169

Keywords:

Alice and Bob want to know if two strings of length $n$ are

almost equal. That is, do they differ on at most $a$ bits?

Let $0\le a\le n-1$.

We show that any deterministic protocol, as well as any

error-free quantum protocol ($C^*$ version), for this problem

requires at least $n-2$ bits of communication.

We show the same bounds for the problem of determining

if two strings differ in exactly $a$ bits.

We also prove a lower bound of $n/2-1$ for error-free $Q^*$ quantum protocols.

Our results are obtained by lower-bounding the ranks of the

appropriate matrices.