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To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…

Many control and detection applications require real-time analysis of signals from sensors, in order to quickly and accurately act upon events revealed by the sensors. Such signal analysis benefits from statistical models of signal and…

Quantum metrology makes use of coherent superpositions to detect weak signals. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by…

We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…

In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…

This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

Sensing static or slowly varying magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging and materials science. Several versatile magnetometry platforms have emerged…

Quantum entanglement, in the form of spin squeezing, is known to improve the sensitivity of atomic sensors to static or slowly varying fields. Sensing transient events presents a distinct challenge, requires different analysis tools, and…

We demonstrate a highly sensitive real-time magnetometry method at two measurement points. This magnetometry method is based on the frequency-division multiplexing of continuous-wave optically detected magnetic resonance. We use two…

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

Nitrogen vacancy (NV) centers in diamonds have been explored for realizing a wide range of sensing applications in the last decade due to their unique quantum properties. Here we realize a compact and portable magnetometer with an ensemble…

The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate…

We present a measurement scheme capable of achieving the quantum limit of parameter estimation using an adaptive strategy that minimizes the parameter's variance at each step. The adaptive rule we propose makes the scheme robust against…

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn),…

Entropy is one of the most fundamental quantities in physics. For systems with few degrees of freedom, the value of entropy provides a powerful insight into its microscopic dynamics, such as the number, degeneracy and relative energies of…

Entanglement entropy has become an important theoretical concept in condensed matter physics, because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental…

Entanglement is the key feature of many-body quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to…

Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…