Noisy metrology: a saturable lower bound on quantum Fisher information

Abstract

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cramér-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision of estimation is introduced. Unlike the bounds previously introduced in the literature, the upper bound is saturable and yields a practical instruction to estimate the parameter through preparing the optimal initial state and optimal measurement. The bound is based on the underling dynamics and its calculation is straightforward and requires only the matrix representation of the quantum maps responsible for encoding the parameter. This allows us to apply the bound to open quantum systems whose dynamics are described by either semigroup or non-semigroup maps. Reliability and efficiency of the method to predict the ultimate precision limit are demonstrated by three main examples.

Improving the precision of frequency estimation via long-time coherences

“…The advantage due to quantum estimation strategies is jeopardized by the interaction of the probing systems with the surrounding environment, potentially reducing the improvement to a constant factor [3][4][5][6]. To overcome this limitation, in recent years several approaches have been put forward, relying on non-negligible spatial [7][8][9] or temporal [10][11][12][13][14][15][16][17][18] correlations in the environment, as well on a particular geometry of the system-environment coupling [19], possibly allowing for error correction techniques [20][21][22][23][24][25][26][27][28] or fault tolerant strategies [29]. These approaches are mostly focused on achieving the best asymptotic scaling of the estimation precision with respect to the number of probes, especially aiming at surpassing the SQL, thus also providing a clear fingerprint of the quantum origin of the obtained enhancement.…”

Nonlinear Quantum Metrology of Many-Body Open Systems

“…Recent progress has been made in noisy quantum metrology to achieve optimal sensitivity [2, [14][15][16][17][18][19][20][21][22]. Nonlinear estimation strategies open yet new frontiers [2,23] and progress has been made towards a general theory [24][25][26][27][28] and its applications, e.g., in Bose-Einstein condensates [29][30][31][32] and optical atomic clocks [33][34][35].…”