Filtering noise with a quantum probe | NIST

J. J. Bollinger

David A. Long, Adam J. Fleisher, Szymon Wójtewicz +1 more

Nicola Dalla Pozza, Stefano Gherardini, Matthias M. Müller +1 more

The success of quantum noise sensing methods depends on the optimal interplay between properly designed control pulses and statistically informative measurement data on a specific quantum-probe observable. To enhance the information content of the data and reduce as much as possible the number of measurements on the probe, the filter orthogonalization method has been recently introduced. The latter is able to transform the control filter functions on an orthogonal basis allowing for the optimal reconstruction of the noise power spectral density. In this paper, we formalize this method within the standard formalism of minimum mean squared error estimation and we show the equivalence between the solutions of the two approaches. Then, we introduce a nonnegative least squares formulation that ensures the nonnegativeness of the estimated noise spectral density. Moreover, we also propose a novel protocol for the design in the frequency domain of the set of filter functions. The frequency-designed filter functions and the nonnegative least squares reconstruction are numerically tested on noise spectra with multiple components and as a function of the estimation parameters.

Emanuel H. Knill

Flavio Salvati, Wilfred Salmon, C. H. W. Barnes +1 more

In quantum metrology, information about unknown parameters θ = ( θ 1 , ... , θ M ) is accessed by measuring probe states ρ ̂ θ . In experimental settings where copies of ρ ̂ θ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high postprocessing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in ρ ̂ θ ⊗ n into m < n copies of a postselected state: ρ ̂ θ ps ⊗ m . Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for m / n arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise. Published by the American Physical Society 2024

Emanuel H. Knill