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arXiv 2110.07613quant-ph
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用于函数估计的最小纠缠协议

Minimum Entanglement Protocols for Function Estimation

Adam Ehrenberg, Jacob Bringewatt, Alexey V. Gorshkov

AI总结:

针对量子传感器网络中 d 个场振幅线性组合的估计问题,论文给出达到量子 Cramér-Rao 界的最优协议族,并刻画至多 k 体纠缠即可最优的充要条件。

摘要:

我们推导了一族最优协议,其最优性意义在于达到量子 Cramér-Rao 界;这些协议用量子传感器网络测量 d 个场振幅的线性组合,而该任务是一般量子传感器网络应用的关键子协议。我们展示了如何在各种约束下从这一族中选择不同协议。主要关注基于纠缠的约束,我们证明了一个令人惊讶的结果:在许多情况下,实现最优性并不需要高度纠缠态。具体而言,我们证明了使用至多 k 体纠缠的最优协议存在的充要条件。我们证明,即使允许使用任意控制和辅助系统,满足这些条件的协议所使用的纠缠量也是可能的最小值。我们的协议需要一定量的含时控制,并且我们表明,一类相关的不含时协议无法对一般函数实现最优标度。

英文摘要:

We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of $d$ field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most $k$-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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