Generalized Uncertainty Principle for Entangled States of two Particles

In this work we determine the consequences of the quantum entanglement of a system of two identical particles when a generalized uncertainty principle (GUP) is considered. GUPs are usually associated with the existence of a minimal length. We focus on the main GUPs (KMM, ADV, Pedram and Nouicer) and then we determine the minimal uncertainties in position induced by those modified GUPs. Our results point out that the minimal uncertainty is reduced by half of its usual value independently of the GUP employed. This implies that the minimal length is also reduced by half. On the other hand, it is generally expected that the minimal length must not depend on physical system. We overcome this apparent paradox by realizing that the entangled system is composed by two particles so that an effective parameter related to the minimal length must be employed.