论文标题
量子通道的纠缠成本的可计算下限
Computable lower bounds on the entanglement cost of quantum channels
论文作者
论文摘要
最近在[Arxiv：2111.02438]中引入了任何量子状态的纠缠成本的一类下限，以称为稳定的鲁棒性和缓和的负性的纠缠形式。在这里，我们将其定义扩展到点对点量子通道，为任何通道的渐近纠缠成本（无论是有限的还是无限的）建立下限。这尤其是导致一个可以计算为半决赛程序的界限，并且可以超越先前已知的下限，包括基于量子相对熵的下限。在证明过程中，我们建立了量子状态纠缠和量子通道的鲁棒性之间的有用联系，这需要几种技术发展，例如在弱* - 操作员范围内的线性线性图中，在痕量类操作员之间有界线性图中，通道的纠缠符合性符合性的鲁棒性较低。
A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438] in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.
