Related papers: A Universal Formulation of Uncertainty Relation fo…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
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…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
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…
An indirect measurement model is constructed for an approximately repeatable, precise position measuring apparatus that violates the assertion, sometimes called the Heisenberg uncertainty principle, that any position measuring apparatus…
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…
We extend the Watanabe--Sagawa--Ueda (WSU) uncertainty relations for measurement errors to infinite-dimensional systems. The original WSU formulation provided a definition of measurement errors with a clear physical interpretation based on…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
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 Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant…
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…
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…
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…
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the…
We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for…
We study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…