Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric formulation of uncertainty principle   A geometric approach to formulate the uncertainty principle between quantum
observables acting on an $N$-dimensional Hilbert space is proposed. We consider
the fidelity between a density operator associated with a quantum system and a
projector associated with an observable, and interpret it as the probability of
obtaining the outcome corresponding to that projector. We make use of
fidelity-based metrics such as angle, Bures and root-infidelity ones, to
propose a measure of uncertainty. The triangle inequality allows us to derive a
family of uncertainty relations. In the case of the angle metric, we re-obtain
the Landau--Pollak inequality for pure states and show, in a natural way, how
to extend it to the case of mixed states in arbitrary dimension. In addition,
we derive and compare novel uncertainty relations when using other known
fidelity-based metrics.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph