Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric Extension of Two-Qubit States   Quantum key distribution uses public discussion protocols to establish shared
secret keys. In the exploration of ultimate limits to such protocols, the
property of symmetric extendibility of underlying bipartite states $\rho_{AB}$
plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible
if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal
state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$.
For a symmetric extendible state $\rho_{AB}$, the first task of the public
discussion protocol is to break this symmetric extendibility. Therefore to
characterize all bi-partite quantum states that possess symmetric extensions is
of vital importance. We prove a simple analytical formula that a two-qubit
state $\rho_{AB}$ admits a symmetric extension if and only if
$\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the
intimate relationship between the symmetric extension problem and the quantum
marginal problem, our result also provides the first analytical necessary and
sufficient condition for the quantum marginal problem with overlapping
marginals.

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The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat