Bell's inequality is a strong criterion to distinguish classic and quantum mechanical aspects of reality. Its violation is the net effect of the non-locality stored in the Heisenberg uncertainty principle (HUP) generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on Bell-like operators of two, and three outcomes, as well as continuous cases, are studied. The achievements claim that the violation quality of Bell's and Bell-like inequalities may be a proper tool to get better understanding of the quantum features of gravity and its effects on reality. Indeed, it is obtained that the current accuracy of Stern-Gerlach experiments implies $\beta_0\ll10^{23}$ .Bell's inequality is a strong criterion to distinguish classic and quantum mechanical aspects of reality. Its violation is the net effect of the non-locality stored in the Heisenberg uncertainty principle (HUP) generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on Bell-like operators of two, and three outcomes, as well as continuous cases, are studied. The achievements claim that the violation quality of Bell's and Bell-like inequalities may be a proper tool to get better understanding of the quantum features of gravity and its effects on reality. Indeed, it is obtained that the current accuracy of Stern-Gerlach experiments implies $\beta_0\ll10^{23}$.

Jun 28, 20210 citations

Quantum Measurements and Non-locality

Sandu Popescu, Nicolas Gisin

Lecture notes in physicsJan 1, 20000 citations

The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

Syed Masood, Mir Faizal, M. Zaid Zaz +3 more

In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.

arXiv:1611.00001Physics Letters BOct 24, 201649 citations

Uncertainty-induced quantum nonlocality

Shao-xiong Wu, Jun Zhang, Chang‐shui Yu +1 more

arXiv:1312.0080Physics Letters ADec 12, 2013106 citations

An uncertainty principle for unimodular quantum groups

Jason Crann, Mehrdad Kalantar

We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the state.We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the state.

arXiv:1404.1276Journal of Mathematical PhysicsJul 28, 201410 citations

Quantum Non-Locality and Universe

P. Achuthan, Narayanankutty Karuppath

Jan 1, 20090 citations

\beta_0\ll10^{23}