Quantum metrology for the Ising Hamiltonian with transverse magnetic field
arXiv:1502.06459 · doi:10.1088/1367-2630/17/7/073032
Abstract
We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with nearest-neighbour interactions and in the pres- ence of a global, transverse, magnetic field. We analytically solve the problem and show that the precision with which one can estimate the magnetic field (interaction strength) given one knows the interaction strength (magnetic field) scales at the Heisenberg limit, and can be achieved by a linear superposition of the vacuum and N free fermion states. In addition, we show that GHZ-type states exhibit Heisenberg scaling in precision throughout the entire regime of parameters. Moreover, we numerically observe that the optimal precision using a product input state scales at the standard quantum limit.
9 pages, 3 figures. Comments are most welcomed. In version 2 we have replaced Section 4 with the analytical results for estimating parameters using GHZ-type states. References have been updated and there is also a discussion concerning the duality of the one-dimensional Ising model. Version 3 is the published version
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