Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decoupling with random diagonal unitaries   We investigate decoupling, one of the most important primitives in quantum
Shannon theory, by replacing the uniformly distributed random unitaries
commonly used to achieve the protocol, with repeated applications of random
unitaries diagonal in the Pauli-$Z$ and -$X$ bases. This strategy was recently
shown to achieve an approximate unitary $2$-design after a number of
repetitions of the process, which implies that the strategy gradually achieves
decoupling. Here, we prove that even fewer repetitions of the process achieve
decoupling at the same rate as that with the uniform ones, showing that rather
imprecise approximations of unitary $2$-designs are sufficient for decoupling.
We also briefly discuss efficient implementations of them and implications of
our decoupling theorem to coherent state merging and relative thermalisation.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th