Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum and classical bounds for two-state overlaps   Suppose we have $N$ quantum systems in unknown states $\lvert\psi_i \rangle
$, but know the value of some pairwise overlaps $\left| \langle \psi_k \lvert
\psi_l \rangle \right|^2$. What can we say about the values of the unknown
overlaps? We provide a complete answer to this problem for three pure states
and two given overlaps, and a way to obtain bounds for the general case. We
discuss how the answer contrasts from that of a classical model featuring only
coherence-free, diagonal states, and describe three applications:
basis-independent coherence witnesses, dimension witnesses, and
characterisation of multi-photon indistinguishability.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio