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The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…
The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
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…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
We discuss the uncertainty relation for the azimuthal angle $\phi$ and the $z$-component of the angular momentum $L_z$. To this end we derive the uncertainty relation for an arbitrary pair of observables and discuss the conditions for its…
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…
The purpose of this note is to point out ambiguities that appear in the calculation of angular momentum and its radiated counterpart when some simple formulae are used to compute them. We illustrate, in two simple different examples, how…
We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.
Accurate prediction of pressure and velocity fluctuations in turbulent flows is essential for understanding flow-induced vibration and structural fatigue. This study investigates the role of turbulence model parameter uncertainty in such…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…
The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…
By preparing an input state and measuring an observable for the output state, we can measure a quantum channel. Following the formulation given by Xiao et al., we study an uncertainty relation for ancilla-free measurements of random unitary…
The asymmetry in the time delay for light rays propagating on opposite sides of a spinning body is analyzed. A frequency shift in the perceived signals is found. A practical procedure is proposed for evidencing the asymmetry, allowing for a…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
We present a new geometric formulation of uncertainty relation valid for any quantum measurements of statistical nature. Owing to its simplicity and tangibility, our relation is universally valid and experimentally viable. Although our…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
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…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…