Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simultaneous Communication Protocols with Quantum and Classical Messages   We study the simultaneous message passing (SMP) model of communication
complexity, for the case where one party is quantum and the other is classical.
We show that in an SMP protocol that computes some function with the first
party sending q qubits and the second sending c classical bits, the quantum
message can be replaced by a randomized message of O(qc) classical bits, as
well as by a deterministic message of O(q c log q) classical bits. Our proofs
rely heavily on earlier results due to Scott Aaronson.
  In particular, our results imply that quantum-classical protocols need to
send Omega(sqrt{n/log n}) bits/qubits to compute Equality on n-bit strings, and
hence are not significantly better than classical-classical protocols (and are
much worse than quantum-quantum protocols such as quantum fingerprinting). This
essentially answers a recent question of Wim van Dam. Our results also imply,
more generally, that there are no superpolynomial separations between
quantum-classical and classical-classical SMP protocols for functional
problems. This contrasts with the situation for relational problems, where
exponential gaps between quantum-classical and classical-classical SMP
protocols are known. We show that this surprising situation cannot arise in
purely classical models: there, an exponential separation for a relational
problem can be converted into an exponential separation for a functional
problem.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex