Quantum Metrology and Many-Body Decoherence.

We introduce a scheme for the quantum simulation of many-body decoherence that relies on the unitary evolution generated by a stochastic Hamiltonian including $k$-body interactions \footnote{A. Chenu, M. Beau, J. Cao, and A. del Campo, Quantum Simulation of Many-Body Decoherence: Noise as a Resource, arxiv/1608.01317 (2016).}. We propose to modulate the strength of the interactions with a stochastic process, and show that the dynamics of the noise-averaged density matrix is effectively open and governed by $k$-body Lindblad operators. Our proposal can be readily implemented on a variety of quantum platforms such as optical lattices, superconducting circuits, and trapped ions. It also has interesting applications in quantum metrology. After deriving the Quantum Cram\'{e}r-Rao bound for quantum open systems, we provide the conditions for robustness of the Heisenberg limit in the presence of many-body decoherence.