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arXiv · 0710.0285

Quantum-limited metrology with product states

Sergio Boixo·Animesh Datta·Steven T. Flammia·Anil Shaji·Emilio Bagan·Carlton M. Caves
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Abstract

We study the performance of initial product states of n-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body (k << n) 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.

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Sergio Boixo, Animesh Datta, Steven T. Flammia, Anil Shaji, Emilio Bagan, Carlton M. Caves. 2007-10-20. Quantum-limited metrology with product states. https://doi.org/10.1103/physreva.77.012317

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