GHZ states as near-optimal states for reference frame alignment

Abstract

Let two coordinate systems, in possession of Alice and Bob, be related to each other by an unknown rotation $R\in SO(3)$. Alice is to send identical states $|ψ_0\ra$ to Bob who will make measurements on the received state and will determine the rotation $R$. The task of Bob is to estimate these parameters of the rotation $R$ by the best possible measurements. Based on the Quantum Fisher Information, we show that Greenberger-Horne-Zeilinger (GHZ) states are near optimal states for this task. Compared to the optimal states proposed before, the advantage of $GHZ$ states are that they can be more easily prepared experimentally, and more importantly, we show concrete measurements which will allow Bob to determine the rotation $R$. We also study the robustness of these states in keeping their encoded information, against common sources of noises.

arXiv comment25 pages, three figures, a measurement procedure is added to determine the frame of reference from the GHZ state received

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