Related papers: Minimum uncertainty states and squeezed states fro…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
Recently, Zheng constructs a quantum-control-assisted multipartite variance-based uncertainty relation, which successfully extends the conditional uncertainty relation to the multipartite case [Annalen der physik, 533, 2100014 (2021)]. We…
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…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range…
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 note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
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…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
The Heisenberg position-momentum uncertainty principle shares with the equivalence principle the role of main pillar of our current description of nature. However, in its original formulation it is inconsistent with special relativity, and…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…
The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present…
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…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…