Decoherence in high energy collisions as renormalization group flow

TL;DR

This paper addresses spin decoherence in high-energy collisions due to final-state radiation by unifying Soft-Collinear Effective Theory (SCET) with open quantum systems. The authors show that the renormalization group (RG) evolution of the final-state spin density matrix defines a quantum channel, with the RG scale parameter $t=\log(Q\delta/\mu)$ governing Markovian information loss and enabling a factorization of decoherence effects from detector resolution. In a concrete QED-like calculation for a fermion pair, they derive Kraus operators corresponding to a phase-flip channel, obtaining a predictive entanglement suppression $\mathcal{C}_{\text{final}} \le \mathcal{C}(0) (Q\delta/m)^{-\alpha/\pi}$ and $\mathcal{C}(t) = \mathcal{C}(0) e^{-\alpha/\pi t}$, with the rate set by the coupling $\alpha$. They discuss the generalization to QCD and argue the framework provides a systematically improvable tool for predicting entanglement loss in hadronic final states and connecting theory with experimental detector capabilities.

Abstract

The unification of quantum information science and collider physics is opening a new frontier in high-energy experiments, making a systematic understanding of decoherence a critical challenge. We present a framework to systematically compute spin decoherence from final-state radiation by combining soft-collinear effective theory and open quantum system techniques. We demonstrate that the renormalization group (RG) evolution of the final-state spin density matrix constitutes a quantum channel, where the RG flow parameter, rather than time, drives a Markovian loss of quantum information. Our approach incorporates explicit detector resolution parameters, allowing a direct connection between experimental capabilities and the preservation of quantum coherence. Applying this formalism to a fermion pair ($f\bar{f}$) in the high-energy limit with QED-like final-state radiation, we provide the first systematically RG-improved prediction for decoherence as a function of experimental resolution, revealing the underlying decoherence mechanism to be a phase-flip channel. This work establishes an essential theoretical tool for future precision measurements of quantum phenomena in high-energy collisions and offers a new perspective on the interplay between RG flow and decoherence of open quantum systems.

Figures (5)

• Figure 1: Schematic illustration of spin entanglement generation and loss in two-qubit quantum systems at colliders. The fermion pair is entangled at production but undergoes decoherence due to unresolved soft and collinear emissions.
• Figure 2: Schematic representation of factorization, the scale separation, and the RG flow in our calculation. Note that we choose $Q\beta>Q\delta$ for illustrative purposes only.
• Figure 3: RG evolution as a phase-flip channel. Left: Bloch-sphere representation of decoherence in the $\{\ket{+-}, \ket{-+}\}$ subspace, with lighter shading indicating reduced spin correlations. $\ket{\phi_+} = (\ket{+-}+\ket{-+})/\sqrt{2}$ is a maximally-entangled state (and so are all points on the equator). Right: The corresponding picture of spin decoherence driven by collinear photon emissions (green lines).
• Figure 4: The evolution of concurrence $\mathcal{C}(\rho_{\text{eff}})$ as a function of RG scale $t$ for varying coupling strengths $\alpha$ in the range $[0.02, 0.10]$, assuming $\mathcal{C}(0)=1$ and Eq. \ref{['eq:conevo']} holds. Varying $\alpha$ illustrates the general coupling dependence of decoherence, with stronger interactions leading to faster suppression of entanglement.
• Figure 5: The final concurrence $\mathcal{C}_{\rm final}$ as a function of angular resolution $\delta$, assuming $\mathcal{C}(0)=1$ (initially maximally entangled) and the inequality in Eq. \ref{['eq:con_final']} is saturated. As an example, the center-of-mass energy is fixed at $Q = 125~\text{GeV}$, the fermion mass set to $m_\tau \approx 1.777~\text{GeV}$. The three lines correspond to different coupling strengths: $\alpha=1/10$ (orange), $\alpha=1/50$ (dark magenta), and $\alpha=1/137$ (dark cyan).