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arXiv:2512.17328

The Standard Model Symmetry and Qubit Entanglement

Jochen Szangolies

quant-phSubmitted Dec 19, 2025• Announced Dec 22, 2025
arXivHTMLPDF

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.

DOI
10.3390/e27060569
Comments
23 pages, 4 figures

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Abstract Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged U(N ) matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain ‘off-diagonal’ matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk ‘area law’ contribution to the entanglement entropy. All of these entropies are regularized by finite N.
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Abstract We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterization of when it is consistent to treat a quantum subsystem classically in such a limit, namely: In any quantum state corresponding to a definite classical state in the classical limit, the reduced density matrix of the subsystem must be approximately proportional to a projection operator, and the projection operators for different classical subsystem states must obey an approximate mutual orthogonality condition. These are strong constraints on the entanglement structure of classical states. They generically give rise to fundamentally nonlocal classical degrees of freedom, which may nevertheless be accounted for using a completely local kinematical description, if one gauges this description in the right way. The mechanism we describe is very general, but for concreteness we exhibit a toy example involving three entangled spins at high angular momentum, and we also describe a significant group-theoretic generalization of this toy example. Finally, we give evidence that this phenomenon plays a role in the emergence of bulk diffeomorphism invariance in gravity.
A bstract We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual c = 1 matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon, extending the construction from black hole horizons to arbitrary subregions. Motivated by the absence of the gravitational area-like term in previous analyses of entanglement entropy in the c = 1 model, we compute the effect on the entanglement entropy of the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations, finding that it cannot account for the area-like term. We offer preliminary comments on the possible origin of the area term in the non-singlet sectors of the theory.