Optimal state for keeping reference frames aligned and the Platonic solids

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Kolenderski, Piotr
Demkowicz-Dobrzanski, Rafal
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The optimal N qubit states featuring highest sensitivity to small misalignment of cartesian reference frames are found using the Quantum Cramer-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J=N/2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.
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Quantum Physics
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