General optimality of the Heisenberg limit for quantum metrology

Marcin Zwierz, Carlos A. Pérez-Delgado and Pieter Kok

Physical Review Letters 105, 180402 (2010)

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We demonstrate that the Heisenberg limit is optimal for all parameter estimation procedures in quantum metrology, but it requires careful consideration as to which resource is appropriate for expressing the scaling behaviour of the mean square error. Rather than a generalized uncertainty relation, the Heisenberg limit is an expression of the Margolus-Levitin bound on the speed of dynamical evolution for quantum states.

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