arXiv subjects

Markus Sifft

Publications and source records attributed to Markus Sifft.

3 recordsLinked to original sources

arXiv2025

Correct Estimation of Higher-Order Spectra: From Theoretical Challenges to Practical Multi-Channel Implementation in SignalSnap

Higher-order spectra (Brillinger's polyspectra) offer powerful methods for solving critical problems in signal processing and data analysis. Despite their significant potential, their practical use has remained limited due to unresolved mathematical issues in spectral estimation, including the absence of unbiased and consistent estimators and the high computational cost associated with evaluating multidimensional spectra. Consequently, existing tools frequently produce artifacts, no existing software library correctly implements Brillinger's cumulant-based trispectrum, or fail to scale effectively to real-world data volumes, leaving crucial applications like multi-detector spectral analysis largely unexplored. In this paper, we revisit higher-order spectra from a modern perspective, addressing the root causes of their historical underuse. We reformulate higher-order spectral estimation using recently derived multivariate k-statistics, yielding unbiased and consistent estimators that eliminate spurious artifacts and precisely align with Brillinger's theoretical definitions. Our methodology covers single- and multi-channel spectral analysis up to the bispectrum (third order) and trispectrum (fourth order), enabling robust investigations of inter-frequency coupling, non-Gaussian behavior, and time-reversal symmetry breaking. Additionally, we introduce quasi-polyspectra to uncover non-stationary, time-dependent higher-order features. We implement these new estimators in SignalSnap, an open-source GPU-accelerated library capable of efficiently analyzing datasets exceeding hundreds of gigabytes within minutes. In applications such as continuous quantum measurements, SignalSnap's rigorous estimators enable precise quantitative matching between experimental data and theoretical models.

physics.data-an↗

arXiv2024

Revealing Hidden States in Quantum Dot Array Dynamics: Quantum Polyspectra Versus Waiting Time Analysis

Quantum dots (QDs) are pivotal for the development of quantum technologies, with applications ranging from single-photon sources for secure communication to quantum computing infrastructures. Understanding the electron dynamics within these QDs is essential for characterizing their properties and functionality. Here, we show how by virtue of the recently introduced quantum polyspectral analysis of transport measurements, the complex transport measurements of multi-electron QD systems can be analyzed. This method directly relates higher-order temporal correlations of a raw quantum point contact (QPC) current measurement to the Liouvillian of the measured quantum system. By applying this method to the two-level switching dynamics of a double QD system, we reveal a hidden third state, without relying on the identification of quantum jumps or prior assumptions about the number of involved quantum states. We show that the statistics of the QPC current measurement can identically be described by different three-state Markov models, each with significantly different transition rates. Furthermore, we compare our method to a traditional analysis via waiting-time distributions for which we prove that the statistics of a three-state Markov model is fully described without multi-time waiting-time distributions even in the case of two level switching dynamics. Both methods yield the same parameters with a similar accuracy. The quantum polyspectra method, however, stays applicable in scenarios with low signal-to-noise, where the traditional full counting statistics falters. Our approach challenges previous assumptions and models, offering a more nuanced understanding of QD dynamics and paving the way for the optimization of quantum devices.

quant-ph↗

arXiv2021

Random-time quantum measurements

The analysis of a continuous measurement record $z(t)$ poses a fundamental challenge in quantum measurement theory. Different approaches have been used in the past as records can, e.g., exhibit predominantly Gaussian noise, telegraph noise, or clicks at random times. The last case may appear as photon clicks in an optical spin noise measurement at very low probe laser power. Here we show that such random-time quantum measurements can similarly to the first two cases be analyzed in terms of higher-order temporal correlations of the detector output $z(t)$ and be related to the Liouvillian of the measured quantum system. Our analysis in terms of up to fourth-order spectra (quantum polyspectra) shows that this new type of spectra reveals the same valuable information as previously studied higher-order spectra in case of usual continuous quantum measurements. Surprisingly, broad-band system dynamics is revealed even for deliberately low average measurement rates. Many applications are envisioned in high-resolution spectroscopy, single-photon microscopy, circuit quantum electrodynamics, quantum sensing, and quantum measurements in general.

quant-ph↗