Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting multipartite entanglement structure with minimal resources   Recently, there are tremendous developments on the number of controllable
qubits in several quantum computing systems. For these implementations, it is
crucial to determine the entanglement structure of the prepared multipartite
quantum state as a basis for further information processing tasks. In reality,
evaluation of a multipartite state is in general a very challenging task owing
to the exponential increase of the Hilbert space with respect to the number of
system components. In this work, we propose a systematic method using very few
local measurements to detect multipartite entanglement structures based on the
graph state --- one of the most important classes of quantum states for quantum
information processing. Thanks to the close connection between the Schmidt
coefficient and quantum entropy in graph states, we develop a family of
efficient witness operators to detect the entanglement between subsystems under
any partitions and hence the entanglement intactness. We show that the number
of local measurements equals to the chromatic number of the underlying graph,
which is a constant number, independent of the number of qubits. In reality,
the optimization problem involved in the witnesses can be challenging with
large system size. For several widely-used graph states, such as 1-D and 2-D
cluster states and the Greenberger-Horne-Zeilinger state, by taking advantage
of the area law of entanglement entropy, we derive analytical solutions for the
witnesses, which only employ two local measurements. Our method offers a
standard tool for entanglement structure detection to benchmark multipartite
quantum systems.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat