Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Swiveled R\'enyi entropies   This paper introduces "swiveled Renyi entropies" as an alternative to the
Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333
(2015)]. What distinguishes the swiveled Renyi entropies from the prior
proposal of Berta et al. is that there is an extra degree of freedom: an
optimization over unitary rotations with respect to particular fixed bases
(swivels). A consequence of this extra degree of freedom is that the swiveled
Renyi entropies are ordered, which is an important property of the Renyi family
of entropies. The swiveled Renyi entropies are however generally discontinuous
at $\alpha=1$ and do not converge to the von Neumann entropy-based measures in
the limit as $\alpha\rightarrow1$, instead bounding them from above and below.
Particular variants reduce to known Renyi entropies, such as the Renyi relative
entropy or the sandwiched Renyi relative entropy, but also lead to ordered
Renyi conditional mutual informations and ordered Renyi generalizations of a
relative entropy difference. Refinements of entropy inequalities such as
monotonicity of quantum relative entropy and strong subadditivity follow as a
consequence of the aforementioned properties of the swiveled Renyi entropies.
Due to the lack of convergence at $\alpha=1$, it is unclear whether the
swiveled Renyi entropies would be useful in one-shot information theory, so
that the present contribution represents partial progress toward this goal.

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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat