相关论文: Uncertainty Principles and Vector Quantization
The uncertainty principle is often interpreted by the tradeoff between the error of a measurement and the consequential disturbance to the followed ones, which originated long ago from Heisenberg himself but now falls into reexamination and…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
In this paper, we study the performance of the PCM scheme with linear quantization rule for quantizing finite unit-norm tight frame expansions for $\R^d$ and derive the PCM quantization error without the White Noise Hypothesis. We prove…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
In this short paper a new thought experiment has been introduced to illustrate the famous Heisenberg's uncertainty principle based on Otto-Wiener's experiment (1890) associated with standing light waves. This illustration is quite easy as…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum,…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
Predicting particle trajectories with neural networks (NNs) has substantially enhanced many scientific and engineering domains. However, effectively quantifying and visualizing the inherent uncertainty in predictions remains challenging.…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…