Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds in the quantum cell probe model   We introduce a new model for studying quantum data structure problems -- the
"quantum cell probe model". We prove a lower bound for the static predecessor
problem in the address-only version of this model where we allow quantum
parallelism only over the `address lines' of the queries. The address-only
quantum cell probe model subsumes the classical cell probe model, and many
quantum query algorithms like Grover's algorithm fall into this framework. Our
lower bound improves the previous known lower bound for the predecessor problem
in the classical cell probe model with randomised query schemes, and matches
the classical deterministic upper bound of Beame and Fich. Beame and Fich have
also proved a matching lower bound for the predecessor problem, but only in the
classical deterministic setting. Our lower bound has the advantage that it
holds for the more general quantum model, and also, its proof is substantially
simpler than that of Beame and Fich. We prove our lower bound by obtaining a
round elimination lemma for quantum communication complexity. A similar lemma
was proved by Miltersen, Nisan, Safra and Wigderson for classical communication
complexity, but it was not strong enough to prove a lower bound matching the
upper bound of Beame and Fich. Our quantum round elimination lemma also allows
us to prove rounds versus communication tradeoffs for some quantum
communication complexity problems like the "greater-than" problem. We also
study the "static membership" problem in the quantum cell probe model.
Generalising a result of Yao, we show that if the storage scheme is implicit,
that is it can only store members of the subset and `pointers', then any
quantum query scheme must make $\Omega(\log n)$ probes.

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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th