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We propose a fast and efficient technique to create classes of highlyentangled states of trapped ions, such as arbitrary Dicke states andsuperpositions of them, e.g. NOON states. The ions are initialized in thephonon ground state and are addressed globally with a composite pulse that isresonant with the first motional sideband. The technique operates oncomparatively short time scales, as resonant interactions allow one to use theminimum laser pulse area. The number of single pulses from the compositesequence is equal to the number of ions, thus the implementation complexitygrows only linearly with the size of the system. The approach does not requireindividual addressing of the ions in the trap and can be applied both insideand outside the Lamb-Dicke regime.

Creation of arbitrary Dicke and NOON states of trapped-ion qubits by global addressing with composite pulses