Tensor-network approach for quantum metrology in many-body quantum systems

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions

Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap in the literature on the subject which until now dealt almost exclusively with two extreme cases: almost perfect knowledge (local approach based on Fisher information) and no a priori knowledge (global approach based on covariant measurements). Special attention is paid to a natural a priori probability distribution arising from a diffusion process.Comment: 4 pages, 2 figures (final version

Compatibility in multiparameter quantum metrology

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and non-unitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.Comment: v2: Corrected form of the Holevo Cramer-Rao bound, other minor fixe

Universality of quantum time dilation

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system's Hamiltonian

Phase estimation without a priori knowledge in the presence of loss

We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a function of number of probes, quantum precision enhancement amounts at most to a constant factor improvement over classical strategiesComment: 8 pages, 2 figures, discussion on adaptive strategies adde

Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?

We discuss the monotonicity under local operations and classical communication (LOCC) of systematically constructed quantities aiming at quantification of entanglement properties of multipartite quantum systems. The so-called generalized multipartite concurrences can qualify as legitimate entanglement measures if they are monotonous under LOCC. In the paper we give a necessary and sufficient criterion for their monotonicity.Comment: 7 pages, 1 figure, minor changes - clarity of proofs improve

Quantum interferometry with and without an external phase reference

We discuss the role of an external phase reference in quantum interferometry. We point out inconsistencies in the literature with regard to the use of the quantum Fisher information (QFI) in phase estimation interferometric schemes. We discuss the interferometric schemes with and without an external phase reference and show a proper way to use QFI in both situations.Comment: 4 pages, 2 figures (formulas corrected, conclusions unchanged