Generalized Uncertainty Principle for Entangled States of Two Identical Particles

TL;DR

This paper investigates how quantum entanglement affects the minimal length scale predicted by various generalized uncertainty principles (GUPs) for two identical particles, revealing that entanglement halves the minimal uncertainty and length.

Contribution

It demonstrates that entanglement modifies the minimal length predicted by GUPs, introducing an effective parameter that accounts for the entangled system's properties.

Findings

Minimal uncertainty is reduced by half due to entanglement.

The minimal length associated with GUPs is also halved.

An effective parameter related to entanglement explains the reduction.

Abstract

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. GUP's are usually associated with the existence of a minimal length. We focus on the main GUP's (KMM, ADV, Pedram and Nouicer) and then we determine the minimal uncertainties in position induced by those modified GUP's. 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.