Generalizations of Heisenberg uncertainty relation

Harris Varghese, M. Ravendranadhan

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 process itself. There are reformulation of the uncertainty relations called the generalized uncertainty relations by including the measurement process into the uncertainty relation. HUR gets modified for the case of entangled particles. Here it is shown that the limit of the Generalized Uncertainty Relation (GUR) also reduces for entangled particles. So, GUR also shows similar trend as that of the HUR for entangled particles. Also as entanglement increases, the uncertainty reduces and measurement becomes more precise.

R. Shankar

Yan-Ni Dou, Hong-Ke Du

In this paper, releasing the restriction on operators which are self-adjoint, we propose a Heisenberg-type uncertainty relation and a Schrödinger-type uncertainty relation with any pair of operators on a Hilbert space. A generalization of Luo's theorem [S. Luo, “Heisenberg uncertainty relation for mixed states,” Phys. Rev. A 72, 042110 (2005)] is investigated.

R. Shankar

Людвиг Дмитриевич Фаддеев, O. Yakubovskiĭ

Fang Wan

From heisenberg’s uncertainty relation, generalized uncertainty relation of quantum system under Planck scale is given and thus minimum uncertainty of position is obtained. The significance of generalized uncertainty relation is elaborated further.