Optimal state for keeping reference frames aligned and the Platonic solids

Abstract

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.

References in corpus (7)

• Reference frames, superselection rules, and quantum information
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• A new approach to the Cramer-Rao type bound of the pure state model
• Efficient use of quantum resources for the transmission of a reference frame
• Optimal estimation of group transformations using entanglement
• Estimation of unitary quantum operations
• Optimal encoding and decoding of a spin direction

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