Related papers: Bending The Heisenberg Uncertainty Principle
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Generalizations of coordinate $x$-momentum $p_x$ Uncertainty Principle, with $\Delta x$ and $\Delta p_x$ dependent terms ($\Delta$ denoting standard deviation), $$\Delta x \Delta p_x\geq i\hbar (1+\alpha\Delta p_x^2 +\beta \Delta x^2)$$…
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been missing in the literature. We investigate the sharp…
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…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
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…
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…
A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
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…