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We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is…
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well known measure of complexity in classical systems and which is valid for both pure and mixed states…
It can be difficult to identify ways to reduce the complexity of large models whilst maintaining predictive power, particularly where there are hidden parameter interdependencies. Here, we demonstrate that the analysis of model sloppiness…
The continuous monitoring of a quantum system strongly influences the emergence of chaotic dynamics near the transition from the quantum regime to the classical regime. Here we present a feedback control scheme that uses adaptive…
We study non-equilibrium steady states and recurrence times in noisy, stroboscopically monitored qubit systems using complete measurements. In the noiseless limit, recurrence times are integer-quantized, with dips to lower integers when…
Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
Stochastic models are widely used to verify whether systems satisfy their reliability, performance and other nonfunctional requirements. However, the validity of the verification depends on how accurately the parameters of these models can…
We propose that weak continuous probing may be exploited to determine and define quantum phases of complex many-body systems based on the measurement record alone. We test the resulting phase criterion in numerical simulations of…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite…
The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition,…
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A…
We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue the state, unlike for the case of…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
This paper considers links between the original risk-sensitive performance criterion for quantum control systems and its recent quadratic-exponential counterpart. We discuss a connection between the minimization of these cost functionals…
Dynamical instabilities can amplify small perturbations into measurable signals, offering a route to quantum-enhanced sensing. This mechanism was experimentally demonstrated in a collective-spin system with quadratic interactions, described…
We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes -- i.e., we compute spacetime correlation functions conditioned on a fixed,…
We introduce a new measure called reduced entropy of sublattice to quantify entanglement in spin, electron and boson systems. By analyzing this quantity, we reveal an intriguing connection between quantum entanglement and quantum phase…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…