Post-selected flavor entanglement in pion–pion scattering

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 $${|{++}\rangle }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> and $${|{--}\rangle }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mrow> <mml:mo>-</mml:mo> <mml:mo>-</mml:mo> </mml:mrow> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> 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 $$\theta =\pi /2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . The analysis demonstrates that isospin-channel dominance plays a central role in shaping the entanglement structure: the $$I=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> 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.