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We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a rigorous generalization of known results for optimal initial states and upper bounds on measurement precision which can only be saturated if pure states are available. In particular, we provide a generalization to mixed states of an upper bound on measurement precision for time-dependent Hamiltonians that can be saturated with optimal Hamiltonian control. These results make precise and reveal the full potential of mixed states for quantum metrology., Comment: 18 pages, 6 figures

We theoretically investigate the possibility of performing high precision estimation of an externally imposed acceleration using scalar bosons in a single-well trap. We work at the level of a two-mode truncation, valid for weak to intermediate two-body interaction couplings.The splitting process into two modes is in our model entirely caused by the interaction between the constituent bosons and is hence neither due to an externally imposed double-well potential nor due to populating a spinor degree of freedom. The precision enhancement gained by using various initial quantum states using a two-mode bosonic system is well established. Here we therefore instead focus on the effect of the intrinsic dynamics on the precision, where, in a single well, the Hamiltonian assumes a form different from that of the typical double-well case. We demonstrate how interactions can significantly increase the quantum Fisher information maximized over initial states as well as the quantum Fisher information for a fragmented or a coherent state, the two many-body states that can commonly represent the ground state of our system., Comment: 9+{\epsilon} pages of RevTex4-1, 3 figures

We investigate in detail a recently introduced "coherent averaging scheme" in terms of its usefulness for achieving Heisenberg limited sensitivity in the measurement of different parameters. In the scheme, $N$ quantum probes in a product state interact with a quantum bus. Instead of measuring the probes directly and then averaging as in classical averaging, one measures the quantum bus or the entire system and tries to estimate the parameters from these measurement results. Combining analytical results from perturbation theory and an exactly solvable dephasing model with numerical simulations, we draw a detailed picture of the scaling of the best achievable sensitivity with $N$, the dependence on the initial state, the interaction strength, the part of the system measured, and the parameter under investigation.