Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifying unsharpness of observables in an outcome-independent way   Recently, a very beautiful measure of the unsharpness (fuzziness) of the
observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The
measure which is defined in this paper is constructed via uncertainty and does
not depend on the values of the outcomes. There exist several properties of a
set of observables (e.g., incompatibility, non-disturbance) that do not depend
on the values of the outcomes. Therefore, the approach in the above-said paper
is consistent with the above-mentioned fact and is able to measure the
intrinsic unsharpness of the observables. In this work, we also quantify the
unsharpness of observables in an outcome-independent way. But our approach is
different than the approach of the above-said paper. In this work, at first, we
construct two Luder's instrument-based unsharpness measures and provide the
tight upper bounds of those measures. Then we prove the monotonicity of the
above-said measures under a class of fuzzifying processes (processes that make
the observables more fuzzy). This is consistent with the resource-theoretic
framework. Then we relate our approach to the approach of the above-said paper.
Next, we try to construct two instrument-independent unsharpness measures. In
particular, we define two instrument-independent unsharpness measures and
provide the tight upper bounds of those measures and then we derive the
condition for the monotonicity of those measures under a class of fuzzifying
processes and prove the monotonicity for dichotomic qubit observables. Then we
show that for an unknown measurement, the values of all of these measures can
be determined experimentally. Finally, we present the idea of the resource
theory of the sharpness of the observables.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs