Entanglement and the generalized uncertainty principle
We propose that gravity, when formulated in the quantum level, can make quantum effects more pronounced. This is demonstrated by considering the effect of the generalized uncertainty principle or GUP (a consequence of quantum gravity theories) on entanglement (a quantum effect). We apply the GUP to continuous-variable systems. In particular, we study the following cases: the modified uncertainty relation of two identical entangled particles [G. Rigolin, Found. Phys. Lett. 15, 293 (2002)], and the inseparability conditions for entangled particles in the bipartite [Duan et al., Phys. Rev. Lett. 84, 2722 (2000)] and tripartite [van Loock and Furusawa, Phys Rev A 67, 052315 (2003)] cases. Rigolin showed a decrease in the lower bound of the product of the uncertainties of the position and momentum for two identical entangled particles while Duan and van Loock derived inseparability conditions for Einstein‐Podolsky‐Rosen-like (EPR-like) operators. In all three cases, the GUP correction resulted in a higher value of the bounds: a higher lower bound for the Rigolin's result and a higher upper bound for the inseparability condition in Duan and van Loock's relations. In Rigolin's case, the GUP correction decreased the disagreement with the Heisenberg uncertainty relation while in Duan's and Loock's case, the inseparability and entanglement conditions are enhanced. Interestingly, the GUP corrections tend to boost quantum mechanical effects.
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Document Type: Research Article
Publication date: December 14, 2018
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