Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Basis entropy: A useful physical quantity about projective measurement   Projective measurement can increase the entropy of a state $\rho$, the
increased entropy is not only up to the basis of projective measurement, but
also has something to do with the properties of the state itself. In this paper
we define this increased entropy as basis entropy. And then we discuss the
usefulness of this new concept by showing its application in deciding whether a
state is pure or not and detecting the existence of quantum discord. And as
shown in the paper, this new concept can also be used to describe decoherence.

19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg