Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Discrepancy: A Non-Commutative Version of Combinatorial
  Discrepancy   In this paper, we introduce a notion of quantum discrepancy, a
non-commutative version of combinatorial discrepancy which is defined for
projection systems, i.e. finite sets of orthogonal projections, as
non-commutative counterparts of set systems. We show that besides its natural
algebraic formulation, quantum discrepancy, when restricted to set systems, has
a probabilistic interpretation in terms of determinantal processes.
Determinantal processes are a family of point processes with a rich algebraic
structure. A common feature of this family is the local repulsive behavior of
points. Alishahi and Zamani (2015) exploit this repelling property to construct
low-discrepancy point configurations on the sphere.
  We give an upper bound for quantum discrepancy in terms of $N$, the dimension
of the space, and $M$, the size of the projection system, which is tight in a
wide range of parameters $N$ and $M$. Then we investigate the relation of these
two kinds of discrepancies, i.e. combinatorial and quantum, when restricted to
set systems, and bound them in terms of each other.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph