Related papers: On noise-resolution uncertainty in quantum field t…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
Two-level electron-phonon systems with reflection symmetry linearly coupled to one or two phonon modes (exciton and E$\otimes(b_1+b_2)$ Jahn-Teller model) exhibit strong enhancement of quantum fluctuations of the phonon coordinates 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…
The derivation of the Heisenberg Uncertainty Principle (HUP) from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on wave number that exists at the quantum level. It also…
This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…
While the slogan "no measurement without disturbance" has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world…
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics.…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the…
At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position…
The quantum indeterminacy caused by non-commutativity of observables at different times sets a lower bound on the voltage noise power spectrum in any conducting material. This bound is calculated explicitly in the case of semiconductors…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
Information spreads in time. For example, correlations dissipate when the correlated system locally couples to a third party, such as the environment. This simple but important fact forms the known quantum data-processing inequality. Here…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
The uncertainty relation formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable so that their product should be no less than…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…