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arXiv:2409.13030 · Physical review. D/Physical review. D.

Consequences of minimal entanglement in bosonic field theories

Spencer Chang, Gabriel Jacobo

Published Nov 26, 2024• 8 citations
arXivHTMLPDF

Abstract

In this paper, we study a recently discovered connection between scattering that minimally entangles and emergent symmetries. In a perturbative expansion, we have generalized the constraints of minimal entanglement scattering, beyond qubits, to general qudits of dimension d . Interestingly, projecting on any qubit subspaces, the constraints factorize, so that it is consistent to analyze minimal entanglement by looking at all such subspaces. We start by looking at toy models with two scalar fields, finding that minimal entanglement only allows quartic couplings which have instabilities at large field values and no symmetries. For the two Higgs doublet model, by considering H + H − → H + H − scattering, we show that minimal entanglement in this channel does not allow an interacting parameter point with enhanced symmetries. These results show that the connection between minimal entanglement and symmetries depends strongly on the scattering channels analyzed and we speculate on the potential resolutions. Published by the American Physical Society 2024

DOI
10.1103/physrevd.110.096020

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We review recent progress in understanding quantum entanglement generated by 2→22\to 22→2 scattering processes in quantum field theory. Starting from the final-state density matrix, we discuss two complementary approaches to quantifying entanglement: projection onto fixed final-state momenta and tracing out the momentum degrees of freedom. We present analytic results for the concurrence of a mixed two-qubit final state and identify the role of quantum coherences, showing that the real part of the inelastic forward scattering amplitude constitutes a subleading correction to the linearized entropy connected to the relative entropy of coherence. Our framework is illustrated through two phenomenologically relevant examples: high-energy scattering of two flavored scalars in the two-Higgs doublet model and high-energy electron-positron annihilation in QED.
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We study the interplay between crossing symmetry and entanglement in 2→22 \to 22→2 scattering within local quantum field theories that possess an SU(N)SU(N)SU(N) global symmetry. In particular, we recast scattering amplitudes of fixed helicity as quantum operations on the Hilbert space of internal quantum numbers, where the external states play the role of qudits. The entire space of SU(N)SU(N)SU(N)-invariant scattering operators between qudits is spanned by a minimal set of three quantum gates. Recoupling relations among quantum gates are shown to follow directly from the crossing properties of the underlying amplitudes and reveal that entanglement generated from separable states in one channel is necessarily intertwined with another. Consequently, we argue any interacting quantum field theory that realizes an SU(N)SU(N)SU(N) global symmetry must generate entanglement in at least one scattering channel.
The concept of quantum information has provided new ways to investigate the theoretical structure of particle interactions. In particular, it has been shown that extrema of quantum entanglement in scattering and decay processes can be related to symmetries and characteristic properties of particles. We focus on a more specific question: whether the minimization of entanglement entropy generated in scattering processes is systematically related to the suppression of interactions that violate global symmetries or selection rules. We conjecture that the minimization of the entanglement entropy can select the symmetry-preserving point when a new interaction opens a symmetry-violating scattering channel. We investigate the plausibility of this conjecture by considering interactions beyond the Standard Model (BSM) that violate global symmetries or the corresponding selection rules, including lepton number violation, baryon number violation, lepton flavor violation, and flavor-changing neutral currents. We show that, when symmetry-violating interactions open final-state sectors that are orthogonal to the symmetry-preserving sector, the symmetry-preserving point becomes a local minimum of the entanglement entropy. Our results support the possibility that the minimization of entanglement provides a common information-theoretic principle underlying the suppression of BSM phenomena relevant to symmetry-violating interactions.
A bstract We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S -matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.
We investigate quantum entanglement in high-energy 2→22\to 22→2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the SSS-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.