Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum and classical entropic uncertainty relations   How much of the uncertainty in predicting measurement outcomes for
non-commuting quantum observables is genuinely quantum mechanical? We provide a
natural decomposition of the total entropic uncertainty of two non-commuting
observables into a classical component, and an intrinsically quantum mechanical
component. We show that the total quantum component in a state is never lower
or upper bounded by any state-independent quantities, but instead admits
"purity-based" lower bounds that generalize entropic formulations such as the
Maassen-Uffink relation. These relations reveal a non-trivial interplay between
quantum and classical randomness in any finite-dimensional state.

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int