Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Assessing dimensions from evolution   Using tools from classical signal processing, we show how to determine the
dimensionality of a quantum system as well as the effective size of the
environment's memory from observable dynamics in a model-independent way. We
discuss the dependence on the number of conserved quantities, the relation to
ergodicity and prove a converse showing that a Hilbert space of dimension D+2
is sufficient to describe every bounded sequence of measurements originating
from any D-dimensional linear equations of motion. This is in sharp contrast to
classical stochastic processes which are subject to more severe restrictions: a
simple spectral analysis shows that the gap between the required dimensionality
of a quantum and a classical description of an observed evolution can be
arbitrary large.

24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
18
The categories of this paper are: econ