Uncertainties and Entanglement

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.

Jeff Hecht

Otto Charles Anthony Gadea, Gardo Blado

We apply the generalised uncertainty principle (GUP) to the entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. We combine previous work on the Shannon entropy entanglement criterion for bipartite systems and the GUP corrections to the Shannon entropy for a single system to calculate the GUP correction for an entangled bipartite system. As in an earlier paper of the second author, which dealt with variance relations, it is shown that there is an increase in the upper bound for the entanglement condition upon the application of the generalised uncertainty principle. Necessary fundamental concepts of the generalised uncertainty principle, entanglement and the entropic uncertainty relations are also discussed. This paper puts together the concepts of entanglement, entropic uncertainty relations and the generalised uncertainty principle all of which have been separately discussed in pedagogical papers by Schroeder, Majernik et al., Blado et al. and Sprenger.

Otto Charles Anthony Gadea, Gardo Blado

We examine quantum gravity effects by applying the generalized uncertainty principle (GUP) to entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. As in an earlier paper [Blado, Herrera, Erwin arXiv:1706.10013 [quant-ph]] which dealt with variance relations, there is an increase in the upper bound for the entanglement condition upon the application of the generalized uncertainty principle. Fundamental concepts of the generalized uncertainty principle, entanglement and the entropic uncertainty relations are also discussed.