相关论文: A new uncertainty Relation (revised version)
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
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…
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.…
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…
It is shown that an observed length in the potential drops across IQHE samples is a universal length for a given magnetic field strength which has the magnitude equal to the reciprocal magnitude of magnetic length and which results from the…
One brief idea on the extended uncertainty relation and the dynamical quantization of space-time at the Planck scale is presented. The extended uncertainty relation could be a guiding principle toward the renormalizable quantum gravity.…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
In certain circumstances, the uncertainty, $\Delta S [\phi]$, of a quantum observable, $S$, can be bounded from below by a finite overall constant $\Delta S>0$, \emph{i.e.}, $\Delta S [\phi] \geq \Delta S$, for all physical states $\phi$.…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. have shown that the lower bound on the uncertainties of the measurement…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
The uncertainty principle guarantees a non-zero value for the positional uncertainty, $\left\langle \Delta x^2\right\rangle > 0$, even without thermal fluctuations. This implies that quantum fluctuations inherently enhance positional…
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…
In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…