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.
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.
Abstract Some quantum field theories show, in a fundamental or an effective manner, an alternative between a loss of duality for algebras of operators corresponding to complementary regions, or a loss of additivity. In this latter case, the algebra contains some operator that is not generated locally, in the former, the entropies of complementary regions do not coincide. Typically, these features are related to the incompleteness of the operator content of the theory, or, in other words, to the existence of superselection sectors. We review some aspects of the mathematical literature on superselection sectors aiming attention to the physical picture and focusing on the consequences for entanglement entropy (EE). For purposes of clarity, the whole discussion is divided into two parts according to the superselection sectors classification: the present part I is devoted to superselection sectors arising from global symmetries, and the forthcoming part II will consider those arising from local symmetries. Under this perspective, here restricted to global symmetries, we study in detail different cases such as models with finite and Lie group symmetry as well as with spontaneous symmetry breaking or excited states. We illustrate the general results with simple examples. As an important application, we argue the features of holographic entanglement entropy correspond to a picture of an sub-theory with a large number of superselection sectors and suggest some ways in which this identification could be made more precise.
We present a general framework connecting global symmetries to the relativistic S-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize relativistic scattering amplitudes as quantum gates in the bipartite space of states with a discrete quantum number. This formalism naturally recovers and significantly extends previous results on entanglement suppression of the S-matrix, providing a comprehensive approach for studying the emergence of symmetries from an information-theoretic perspective. As a central result, we show that constraining the S-matrix to the span of minimally entangling operators is equivalent to realizing an emergent SU(N) global symmetry.
We study the interplay between crossing symmetry and entanglement in 2→2 scattering within local quantum field theories that possess an 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)-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) global symmetry must generate entanglement in at least one scattering channel.
Symmetry is among the most fundamental and powerful concepts in nature, whose existence is usually taken as given, without explanation. We explore whether symmetry can be derived from more fundamental principles from the perspective of quantum information. Starting with a two-qubit system, we show there are only two minimally entangling logic gates: the identity and the SWAP, which interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the S-matrix in the two-body scattering of fermions in the s-wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the identity and the SWAP. Realizing a minimally entangling S-matrix would give rise to global symmetries, as exemplified in Wigner's spin-flavor symmetry and Schr\"odinger's conformal invariance in low energy quantum chromodynamics. For Nq species of qubit, the identity gate is associated with an [SU(2)]Nq symmetry, which is enlarged to SU(2Nq) when there is a species-universal coupling constant.
Abstract Quantum entanglement provides a quantitative measure of nonclassical correlations and plays a central role in quantum information theory. Identifying and quantifying the mechanisms by which fundamental interactions generate or suppress entanglement is therefore of conceptual interest. In this work, flavor entanglement generated in pion–pion scattering is analyzed within a post-selected framework, in which the outgoing two-pion state is conditioned on fixed asymptotic momenta. The analysis is carried out in the isospin-symmetric limit using chiral perturbation theory, including one-loop corrections to the scattering amplitude. A general formalism is developed to quantify post-selected flavor entanglement through the von Neumann entropy of the reduced flavor density matrix, expressed in terms of a flavor tensor characterizing the initial state. This framework is applied to initially unentangled charged two-pion states. Except for the ∣++⟩ | + + ⟩ and ∣−−⟩ | - - ⟩ channels, which remain unentangled due to isospin conservation, the post-selected final states exhibit nontrivial flavor entanglement and behave effectively as entangled qubits or qutrits. The entanglement is maximal near threshold and typically peaks at scattering angles close to θ=π/2 θ = π / 2 . The analysis demonstrates that isospin-channel dominance plays a central role in shaping the entanglement structure: the I=0 I = 0 channel drives generic initial states toward highly entangled qutrit configurations after scattering and post-selection. Conversely, suitably chosen initial superpositions can undergo a reduction of entanglement, showing that the strong interaction can act both as a generator and a suppressor of quantum correlations. One-loop corrections quantitatively redistribute entanglement across phase space, sharpening angular structures that appear more diffuse at tree level.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.