Entanglement is recognized as a key resource for quantum computation¹ and quantum cryptography². For quantum metrology, the use of entangled states has been discussed^{3, 4, 5} and demonstrated⁶ as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection⁷ and for the measurement of scattering lengths⁸. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment⁹. Such 'decoherence-free subspaces' (ref. 10) protect quantum information and yield significantly enhanced coherence times¹¹. Here we use a decoherence-free subspace with specifically designed entangled states¹² to demonstrate precision spectroscopy of a pair of trapped Ca⁺ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements—a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.

1. Institut für Experimentalphysik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria
2. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria

Correspondence to: C. F. Roos^1,2 Correspondence and requests for materials should be addressed to C.F.R. (Email: christian.roos@uibk.ac.at).

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