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Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…

Quantum Physics · Physics 2025-12-23 Minyi Huang , Ray-Kuang Lee

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Abel Camacho

A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…

Quantum Physics · Physics 2016-09-08 D. A. Trifonov

Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…

Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg…

Quantum Physics · Physics 2017-02-01 Seiji Kosugi

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation…

Quantum Physics · Physics 2013-05-24 N. D. Hari Dass , Tabish Qureshi , Aditi Sheel

It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…

Quantum Physics · Physics 2014-01-17 Kazuo Fujikawa

Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…

High Energy Physics - Phenomenology · Physics 2010-04-05 R. Akhoury , Y. -P. Yao

Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…

Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…

Quantum Physics · Physics 2015-07-31 Patrick J. Coles , Fabian Furrer

The Heisenberg uncertainty principle and its extensions are all still inequalities form which hold the superior approximate estimations. Based on quantum covariant Poisson bracket theory, we propose quantum geomertainty relation to modify…

Quantum Physics · Physics 2023-10-24 Gen Wang

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…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Paul S. Wesson

Recently it was shown in [New J. Phys. 8, 330 (2006)] that the three dimensional Heisenberg uncertainty principle might be signifficantly sharpened if the relevant quantum state describes the particle in a central potential. I extend that…

Quantum Physics · Physics 2015-06-03 Łukasz Rudnicki

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 Physics · Physics 2016-09-19 Luca Nanni

The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…

Quantum Physics · Physics 2017-05-22 Wenchao Ma , Bin Chen , Ying Liu , Mengqi Wang , Xiangyu Ye , Fei Kong , Fazhan Shi , Shao-Ming Fei , Jiangfeng Du

Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…

Quantum Physics · Physics 2020-10-19 Krzysztof Urbanowski

The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…

High Energy Physics - Phenomenology · Physics 2026-01-29 Ezequiel Valero , Hector Gisbert , Victor Ilisie

Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…

Quantum Physics · Physics 2019-01-23 Paul Busch , Oliver Reardon-Smith

The Heisenberg uncertainty relation is derived for relativistic electrons described by the Dirac equation. The standard nonrelativistic lower bound $3/2\hbar$ is attained only in the limit and the wave function that reproduces this value is…

Quantum Physics · Physics 2019-12-17 Iwo Bialynicki-Birula , Zofia Bialynicka-Birula

Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for contemporary researches in quantum foundations and quantum information science. Going beyond, here we report the first experimental test of…

Quantum Physics · Physics 2022-11-24 Ya-Li Mao , Hu Chen , Chang Niu , Zheng-Da Li , Sixia Yu , Jingyun Fan