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In this paper we explore the possibility of performing Heisenberg limitedquantum metrology of a phase, without any prior, by employing only maximallyentangled states. Starting from the estimator introduced by Higgins et al. inNew J. Phys. 11, 073023 (2009), the main result of this paper is to produce ananalytical upper bound on the associated Mean Squared Error which ismonotonically decreasing as a function of the square of the number of quantumprobes used in the process. The analysed protocol is non-adaptive and requiresin principle (for distinguishable probes) only separable measurements. Weexplore also metrology in presence of a limitation on the entanglement size andin presence of loss.

Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error