Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resource Marginal Problems   We introduce the resource marginal problems, which concern the possibility of
having a resource-free target subsystem compatible with a given collection of
marginal density matrices. By identifying an appropriate choice of resource $R$
and target subsystem T, our problems reduce, respectively, to the well-known
marginal problems for quantum states and the problem of determining if a given
quantum system is a resource. More generally, we define a set of marginal
states to be resource-free incompatible with a target subsystem T if all global
states compatible with this set must result in a resourceful state in T. We
show that this incompatibility induces a resource theory that can be quantified
by a monotone. We derive necessary and sufficient conditions for this monotone
to be a finite conic program and further show, via the corresponding witnesses,
that resource-free incompatibility is equivalent to an operational advantage in
some subchannel discrimination task. Via our framework, a clear connection can
be established between any marginal problem (that involves some notion of
incompatibility) for quantum states and a resource theory for quantum states.
In addition, the universality of our framework leads, for example, to an
immediate, quantitative understanding of the incompatibility associated with
the recently-proposed entanglement marginal problems. As further applications,
we provide the first example showing a form of transitivity of nonlocality
(steerability) for quantum states. We discuss also the analogous framework in
the dynamical regime and establish a set of theoretical results that closely
mirror those obtained for a resource theory for quantum states. Again, they
allow us to recover a wide variety of results related to the studies of channel
marginal problems, channel resource theories, etc.

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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con