Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cauchy-Schwarz inequality and particle entanglement   The Glauber-Sudarshan $P$-representation is used in quantum optics to
distinguish between semi-classical and genuinely quantum electromagnetic
fields. We employ the analog of the $P$-representation to show that the
violation of the Cauchy-Schwarz inequality for the second-order correlation
function is a proof of entanglement between identical massive bosons. The
presented derivation is valid both in systems with fixed and fluctuating number
of particles. Thanks to the recent advances in techniques of detecting
positions of separate particles, the violation of the Cauchy-Schwarz inequality
can be used as a simple entanglement criterion in various many-body quantum
systems.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
18
The categories of this paper are: econ