Abstract
We study the performance of initial product states of -body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear -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 , and for initial product states, it scales as . We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian , implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the scaling for ; 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 sensitivity scaling for initial product states.
- Received 20 October 2007
DOI:https://doi.org/10.1103/PhysRevA.77.012317
©2008 American Physical Society