AI 中文总结
该研究将量子态转移推广至完美$(s,r)$-态转移，刻画了纠缠度保持与否的条件，提出最大化保真度的算法，并进行了灵敏度分析。
AI 中文摘要
在过去的二十年里，关于量子自旋网络中的量子态转移问题已经进行了大量研究。人们可以用无向图来模拟这样一个由相互作用的量子比特组成的系统，并研究顶点到顶点的动力学。最近，这一设置被放宽，允许在两个顶点态的线性组合之间进行动力学，即从 $\mathbf u = \mathbf e_a + s \mathbf e_b$ 到 $\mathbf \mu=\mathbf e_{\alpha} + r \mathbf e_{\beta}$，其中 $r=s$ 要么是 $-1$（对应于对态转移），要么是 $+1$（对应于加态转移），或者更近地，$r=s$ 取任意实数（对应于 $s$-对态转移）。在这里，我们将 $s$-对态转移的研究扩展到\textit{完美 $(s,r)$-态转移}，即从 $\mathbf u = \mathbf e_a + s \mathbf e_b$ 到 $\mathbf \mu=\mathbf e_{\alpha} + r \mathbf e_{\beta}$（在某种伸缩下）的完美态转移，其中 $r,s\in \mathbb C$。我们确定了具有完美 $(s,r)$-态转移的图的无限族，并提供了当 $|r|= |s|$ 和当 $|r|\neq |s|$ 时的特征刻画，展示了顶点态之间纠缠度何时被保留，以及何时不被保留的情况。后者尤为重要，因为它代表了从一个纠缠量子比特对到另一个纠缠量子比特对的完美态转移，而纠缠度不必相同——事实上，它可以被设置成“增强”（增加）纠缠。我们提供了一种算法，该算法在给定 $s$-对态 $\mathbf u$ 和固定时间 $t$ 下，找到具有两个非零分量的向量，该向量最大化转移保真度。最后，我们提供了关于读出时间误差的完美 $(s,r)$-态转移的灵敏度分析。
英文摘要
Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirected graph, and studying vertex-to-vertex dynamics. This setup has recently been relaxed to allow for dynamics between linear combinations of two vertex states, i.e.\ from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$, where $r=s$ is either $-1$ (which corresponds to pair state transfer) or $+1$ (which corresponds to plus state transfer), or more recently $r=s$ is taken to be any real number (which corresponds to $s$-pair state transfer). Here, we broaden the investigation of $s$-pair state transfer to \textit{perfect $(s,r)$-state transfer}, which is perfect state transfer from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf μ=\mathbf e_α + r \mathbf e_β$ (up to some dilation) where $r,s\in \mathbb C$. We identify infinite families of graphs with perfect $(s,r)$-state transfer and provide characterizations of cases when $|r|= |s|$ and when $|r|\neq |s|$, showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time $t$ starting from a given $s$-pair state $\mathbf u$. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect $(s,r)$-state transfer.
Comments20 pages
