Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clean quantum and classical communication protocols   By how much must the communication complexity of a function increase if we
demand that the parties not only correctly compute the function but also return
all registers (other than the one containing the answer) to their initial
states at the end of the communication protocol? Protocols that achieve this
are referred to as clean and the associated cost as the clean communication
complexity. Here we present clean protocols for calculating the Inner Product
of two $n$-bit strings, showing that (in the absence of pre-shared
entanglement) at most $n+3$ qubits or $n+O(\sqrt{n})$ bits of communication are
required. The quantum protocol provides inspiration for obtaining the optimal
method to implement distributed CNOT gates in parallel whilst minimizing the
amount of quantum communication. For more general functions, we show that
nearly all Boolean functions require close to $2n$ bits of classical
communication to compute and close to $n$ qubits if the parties have access to
pre-shared entanglement. Both of these values are maximal for their respective
paradigms.

20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th