论文标题
验证分阶段dicke状态
Verification of phased Dicke states
论文作者
论文摘要
迪克状态是具有真正多部分纠缠的量子状态的典型例子。它们是许多量子信息处理任务中的宝贵资源，包括多部分量子通信和量子计量学。分阶段的dicke状态是Dicke态的概括，并包括反对称基础状态作为一个特殊的例子。除了量子信息处理外，这些状态在原子和分子物理学中都有用。在这里，我们建议基于自适应的本地投影测量值，以验证所有相位的迪克州，包括$ w $ state和Qudit Dicke States。要验证不忠$ε$和显着性级别$δ$内的任何$ n $ - 零件分阶段的dicke状态，所需的测试数量仅为$ o（nε^{ - 1} \lnΔ^{ - 1}）$，在$ N $中是线性的，并且比传统的整体构造效率更高。对于$ w $状态，可以将测试的数量进一步简化为$ o（\ sqrt {n} \，ε^{ - 1} \lnδ^{ - 1}）$。此外，我们为任何反对称基础状态构建了最佳协议。所需的测试数量以$ n $单调的方式减少（而不是增加）。这是唯一针对多部分非稳态状态已知的最佳协议。
Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased Dicke states are a generalization of Dicke states and include antisymmetric basis states as a special example. These states are useful in atomic and molecular physics besides quantum information processing. Here we propose practical and efficient protocols based on adaptive local projective measurements for verifying all phased Dicke states, including $W$ states and qudit Dicke states. To verify any $n$-partite phased Dicke state within infidelity $ε$ and significance level $δ$, the number of tests required is only $O(nε^{-1}\lnδ^{-1})$, which is linear in $n$ and is exponentially more efficient than traditional tomographic approaches. In the case of $W$ states, the number of tests can be further reduced to $O(\sqrt{n}\,ε^{-1}\lnδ^{-1})$. Moreover, we construct an optimal protocol for any antisymmetric basis state; the number of tests required decreases (rather than increases) monotonically with $n$. This is the only optimal protocol known for multipartite nonstabilizer states.
