Using Adaptiveness and Causal Superpositions Against Noise in Quantum Metrology.

We derive new bounds on achievable precision in the most general adaptive quantum metrological scenarios. The bounds are proven to be asymptotically saturable and equivalent to the known parallel scheme bounds in the limit of a large number of channel uses. This completely solves a long-standing conjecture in the field of quantum metrology on the asymptotic equivalence between parallel and adaptive strategies. The new bounds also allow us to easily assess the potential benefits of invoking nonstandard causal superposition strategies, for which we prove, similarly to the adaptive case, the lack of asymptotic advantage over the parallel ones.

Quantum Asymmetry and Noisy Multimode Interferometry.

Quantum asymmetry is a physical resource that coincides with the amount of coherence between the eigenspaces of a generator responsible for phase encoding in interferometric experiments. We highlight an apparently counterintuitive behavior that the asymmetry may increase as a result of a decrease of coherence inside a degenerate subspace. We intuitively explain and illustrate the phenomena by performing a three-mode single-photon interferometric experiment, where one arm carries the signal and two noisy reference arms have fluctuating phases. We show that the source of the observed sensitivity improvement is the reduction of correlations between these fluctuations and comment on the impact of the effect when moving from the single-photon quantum level to the classical regime. Finally, we also establish the analogy of the effect in the case of entanglement resource theory.

Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement.

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.

Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology.

Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cramér-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case.