Related papers: A Universally Valid Uncertainty Relation Revisited
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far…
In a recent publication [PRL 111, 160405 (2013)] we proved a version of Heisenberg's error-disturbance tradeoff. This result was in apparent contradiction to claims by Ozawa of having refuted these ideas of Heisenberg. In a direct reaction…
Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…
We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
We propose a new method for generating generalised uncertainty relations (GURs) including the generalised uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalised uncertainty principle (EGUP), previously…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this…
In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its…
We formulate and prove a new, universally valid uncertainty relation for the necessary errors bar widths in any approximate joint measurement of position and momentum.
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…
In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for…