Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds on the Deterministic and Quantum Communication Complexity
  of Hamming Distance   Alice and Bob want to know if two strings of length n are almost equal. That
is, do they differ on \textit{at most} a bits? Let 0\leq a\leq 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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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con