In this paper we explore the possibility of performing Heisenberg limited quantum metrology of a phase, without any prior, by employing only maximally entangled states. Starting from the estimator introduced by Higgins et al. in New J. Phys.~11 , 073023 (2009), the main result of this paper is to produce an analytical upper bound on the associated Mean Squared Error which is monotonically decreasing as a function of the square of the number of quantum probes used in the process. The analyzed protocol is non-adaptive and requires in principle (for distinguishable probes) only separable measurements. We explore also metrology in presence of a limitation on the entanglement size and in presence of loss.

中文翻译：

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利用最大纠缠态实现海森堡缩放：可达到的均方根误差的解析上限

在本文中，我们探索了仅通过最大纠缠态就可以在没有任何先验的情况下执行海森堡有限相量子计量的可能性。从希金斯等人介绍的估计量开始。在New J. Phys。〜11，073023（2009）中，本文的主要结果是在相关的均方误差上产生一个解析上限，该均值随所用量子探针数量的平方而单调递减进行中。分析的协议是非自适应的，原则上（对于可区分的探针）仅要求可分离的测量。我们还探讨了纠缠大小受限和损耗存在的计量学。