arXiv 1809.056412018-09-15quant-phmath-phmath.MP

二分态的对称扩张与玻色扩张

Symmetric vs. bosonic extension for bipartite states

Youning Li, Shilin Huang, Dong Ruan, Bei Zeng

备注：: 10 pages, comments welcome
发表信息：: Phys. Rev. A 99, 012332 (2019)
DOI：: 10.1103/PhysRevA.99.012332

摘要：

如果存在一个具有边值$ρ^{AB_i}=ρ^{AB}, \forall i$的$k+1$ -分状态$ρ^{AB_1B_2\ldots B_k}$，则二分状态$ρ^{AB}$具有$k$ -对称扩展.如果$B_1B_2\ldots B_k$的对称子空间上支持$ρ^{AB_1B_2\ldots B_k}$，则称$k$ -对称扩张为玻色子扩张.了解对称/玻色扩张的结构在量子纠缠理论、量子密钥分发和量子边缘问题中有着广泛的应用。特别地，玻色扩张给出了基于可分性的量子边际问题的更严格的界。通常，已知允许对称扩展的$ρ^{AB}$可以不具有玻色子扩展。在这项工作中，我们表明，当子系统$B$的维数是$2$（即量子比特），$ρ^{AB}$允许$k$ -对称扩展当且仅当它有一个$k$ -玻色子扩展。我们的结果有一个直接的应用到量子边际问题，并指出了一个特殊的结构的量子比特系统的基础上群表示理论。

英文摘要：

A bipartite state $ρ^{AB}$ has a $k$-symmetric extension if there exists a $k+1$-partite state $ρ^{AB_1B_2\ldots B_k}$ with marginals $ρ^{AB_i}=ρ^{AB}, \forall i$. The $k$-symmetric extension is called bosonic if $ρ^{AB_1B_2\ldots B_k}$ is supported on the symmetric subspace of $B_1B_2\ldots B_k$. Understanding the structure of symmetric/bosonic extension has various applications in the theory of quantum entanglement, quantum key distribution and the quantum marginal problem. In particular, bosonic extension gives a tighter bound for the quantum marginal problem based on seperability. In general, it is known that a $ρ^{AB}$ admitting symmetric extension may not have bosonic extension. In this work, we show that when the dimension of the subsystem $B$ is $2$ (i.e. a qubit), $ρ^{AB}$ admits a $k$-symmetric extension if and only if it has a $k$-bosonic extension. Our result has an immediate application to the quantum marginal problem and indicates a special structure for qubit systems based on group representation theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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