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TR04-120 | 22nd November 2004 00:00

Lower bounds on the Deterministic and Quantum Communication Complexity of HAM_n^a



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.

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