Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classically Replaceable Operation   Quantum information science provides powerful technologies beyond the scope
of classical physics. In practice, accurate control of quantum operations is a
challenging task with current quantum devices. The implementation of high
fidelity and multi-qubit quantum operations consumes massive resources and
requires complicated hardware design to fight against noise. An approach to
improving the performance and efficiency is to replace some quantum operations
with tractable classical processing. Despite the common practice of this
approach, rigorous criteria to determine whether a given quantum operation is
replaceable "classically" are still missing. In this work, we define the
classically replaceable operations in four general scenarios. In each scenario,
we provide their necessary and sufficient criteria and point out the
corresponding classical processing. For a practically favourable case of
unitary classically replaceable operations, we show that the replaced classical
processing is deterministic. Beyond that, we regard the irreplaceability with
classical processing as a quantum resource and relate it to the performance of
a channel in a non-local game, as manifested in a robustness measure.

10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin