AI 中文总结
本文证明挤压纠缠的优化无需对条件系统维度设界，并以部分去相位贝尔对为例，说明任何有限维扩展都无法达到其挤压纠缠值。
AI 中文摘要
挤压纠缠是一种可加的双方纠缠度量。对于态 $\rho_{AB}$，它定义为在所有扩展 $\rho_{ABE}$ 上评估的条件互信息 $I(A:B\mid E)$ 的下确界。此前尚未解决的是，用于此优化的条件系统 $E$ 的维度是否存在界限。我们证明不存在这样的基数界。具体而言，我们发现对于两个量子比特上的部分去相位贝尔对，其挤压纠缠无法在任何有限维扩展 $E$ 下实现。该证明的一个关键成分是直接和步骤，从某种意义上说，它对称化了两个纯化系统，同时保持条件互信息不变且相干性不恶化。
英文摘要
Squashed entanglement is an additive bipartite entanglement measure. For a state $ρ_{AB}$, it is defined as the infimum of all conditional mutual information $I(A:B\mid E)$ evaluated on extensions $ρ_{ABE}$. It was unresolved whether there is a bound on the dimension of the conditioning system, $E$, needed for this optimization. We show that no such cardinality bound is possible. Explicitly, we find that the squashed entanglement for a partially dephased Bell pair on two qubits cannot be achieved for any finite dimensional extension $E$. A crucial ingredient of this proof is a direct sum step, which in a sense, symmetrizes two purifying systems while keeping the conditional mutual information unchanged and the coherence no worse.
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