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Quantum-limited metrology with product states

Sergio Boixo, University of New Mexico

(Session 14 : Sunday from 13:00-13:30)

Abstract. We study the performance of generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/n^k, and for initial product states, it scales as 1/n^(k-1/2). We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n^(-3/2)) scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n^(-3/2)) sensitivity scaling for initial product states.