Gühne Otfried, Mao Yuanyuan, Yu Xiao-Dong
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
Phys Rev Lett. 2021 Apr 9;126(14):140503. doi: 10.1103/PhysRevLett.126.140503.
A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties, implying that states with a high fidelity must be entangled. States whose entanglement can be detected in this way are also called faithful. We prove a structural result on the corresponding fidelity-based entanglement witnesses, resulting in a simple condition for faithfulness of a two-party state. For the simplest case of two qubits faithfulness can directly be decided and for higher dimensions accurate analytical criteria are given. Finally, our results show that faithful entanglement is, in a certain sense, useful entanglement; moreover, they establish connections to computational complexity and simplify several results in entanglement theory.
某些纯纠缠态附近的态具有相同的性质，这意味着高保真度的态必定是纠缠的。以这种方式能检测到纠缠的态也被称为忠实态。我们证明了关于相应的基于保真度的纠缠见证者的一个结构结果，得出了一个两方态忠实性的简单条件。对于两个量子比特的最简单情况，忠实性可以直接判定，对于更高维度给出了精确的分析准则。最后，我们的结果表明，在某种意义上，忠实纠缠是有用的纠缠；此外，它们建立了与计算复杂性的联系，并简化了纠缠理论中的几个结果。
