ECCC-Report TR04-120https://eccc.weizmann.ac.il/report/2004/120Comments and Revisions published for TR04-120en-usTue, 21 Dec 2004 16:25:32 +0200
Paper TR04-120
| Lower bounds on the Deterministic and Quantum Communication Complexity of HAM_n^a |
Andris Ambainis,
William Gasarch,
Aravind Srinivasan,
Andrey Utis
https://eccc.weizmann.ac.il/report/2004/120
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.
Tue, 21 Dec 2004 16:25:32 +0200https://eccc.weizmann.ac.il/report/2004/120