Related papers: Universality in Uncertainty Relations for a Quantu…
A smooth function of the second moments of $N$ continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
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.…
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…
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…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
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…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…