Related papers: Uncertainty Relations for Noise and Disturbance in…
In this study, we explore the validity of the original Heisenberg position- momentum uncertainty relation for a macroscopic harmonic oscillator interacting with environmental micro particles. Our results show that, in the quasi-classical…
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…
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…
The Heisenberg uncertainty principle sets a lower bound on the sensitivity of continuous optical measurements of force. This bound, the standard quantum limit, can only be reached when a mechanical oscillator subjected to the force is…
We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the…
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…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Information-theoretic definitions for noise and disturbance in quantum measurements were given in Phys. Rev. Lett. 112, 050401 (2014) and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight…
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…
Common misconceptions on the Heisenberg principle are reviewed, and the original spirit of the principle is reestablished in terms of the trade-off between information retrieved by a measurement and disturbance on the measured system. After…
Heisenberg's uncertainty principle, coherence and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct…
Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations…
Our investigation of the results of the neutron spin experiment by Ehhart et al. demonstrates that their results cannot be understood in accordance with common sense. For example, their results obtained with different measurement errors are…
Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint…
The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that in nearly 90 years there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential…
Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without…