Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate tensorization of the relative entropy for noncommuting
  conditional expectations   In this paper, we derive a new generalisation of the strong subadditivity of
the entropy to the setting of general conditional expectations onto arbitrary
finite-dimensional von Neumann algebras. The latter inequality, which we call
approximate tensorization of the relative entropy, can be expressed as a lower
bound for the sum of relative entropies between a given density and its
respective projections onto two intersecting von Neumann algebras in terms of
the relative entropy between the same density and its projection onto an
algebra in the intersection, up to multiplicative and additive constants. In
particular, our inequality reduces to the so-called quasi-factorization of the
entropy for commuting algebras, which is a key step in modern proofs of the
logarithmic Sobolev inequality for classical lattice spin systems. We also
provide estimates on the constants in terms of conditions of clustering of
correlations in the setting of quantum lattice spin systems. Along the way, we
show the equivalence between conditional expectations arising from Petz
recovery maps and those of general Davies semigroups.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin