  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 analysed 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.
