Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compatibility of subsystem states and convex geometry   The subsystem compatibility problem, which concerns the question of whether a
set of subsystem states are compatible with a state of the entire system, has
received much study. Here we attack the problem from a new angle, utilising the
ideas of convexity that have been successfully employed against the
separability problem. Analogously to an entanglement witness, we introduce the
idea of a compatibility witness, and prove a number of properties about these
objects. We show that the subsystem compatibility problem can be solved
numerically and efficiently using semidefinite programming, and that the
numerical results from this solution can be used to extract exact analytic
results, an idea which we use to disprove a conjecture about the subsystem
problem made by Butterley et al. [Found. Phys. 36 83 (2006)]. Finally, we
consider how the ideas can be used to tackle some important variants of the
compatibility problem; in particular, the case of identical particles (known as
N-representability in the case of fermions) is considered.

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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: eess
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The categories of this paper are: cmp-lg
2
The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph