The Standard Model Symmetry and Qubit Entanglement

Abstract

Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza-Klein proposal aims to recover gauge symmetries by means of dimensional reduction of higher-dimensional gravitational theories. Integrating both, gravitational and gauge degrees of freedom in $3+1$ dimensions may be obtained upon dimensional reduction of higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with $5+1$ and $9+1$ dimensional spacetimes respectively, which are reduced to $3+1$ dimensions upon singling out a preferred complex direction. In the latter case, this reduction is invariant under a residual $SU(3)\times SU(2)\times U(1)/{\mathbb{Z}}_6$ symmetry, the Standard Model gauge group. This motivates a picture in which spacetime emerges from the area law-contribution to the entanglement entropy, while gauge and matter degrees of freedom are due to area law-violating terms. We remark on a possible natural origin of the chirality of the weak force in the given construction. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields.

23 pages, 4 figures

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