Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic
while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger $T$-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.
Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic
while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger T-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.
In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order stabilizer R\'enyi entropy to quantify magic, we study the production of magic states in Quantum Electrodynamics (QED) via 2-to-2 scattering processes involving electrons and muons. Considering all 60 stabilizer initial states, which have zero magic, the angular dependence of magic produced in the final states is governed by only a few patterns, both in the non-relativistic and the ultra-relativistic limits. Some processes, such as the low-energy e−μ−→e−μ− and Bhabha scattering e−e+→e−e+, do not generate magic at all. In most cases the largest magic generated is significantly less than the maximal possible value of log(16/7)≈0.827. The only instance where QED is able to generate maximal magic is the low-energy μ−μ+→e−e+, in the limit me/mμ→0, which is well approximated in nature. Our results suggest QED, although capable of producing maximally entangled states easily, may not be an efficient mechanism for generating quantum advantages.
The property of non-stabiliserness, or ``magic'', is of interest in quantum computing due to its role in developing fault-tolerant quantum algorithms with genuine computational advantage over classical counterparts. There has been much interest in quantifying magic in various physical systems, in order to probe how to produce and enhance it. The production of magic has previously been quantified in gluon and graviton scattering, in the so-called helicity basis relating particle spins with momentum directions. For a basis-independent statement, one should instead use the recently developed concept of non-local non-stabiliserness, and our aim in this paper is to derive how this varies for gluon and graviton scattering processes. Our results show that, for many initial states, including those produced with polarised beams, the helicity basis coincides with a basis in which the non-local magic is manifest, providing a physical motivation for using the helicity basis to study quantum information quantities. However, this property breaks upon adding additional operators to the Yang-Mills Lagrangian, as would be the case in new physics scenarios.
The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant α, the weak mixing angle sin2θw, and the strong coupling αs. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces sin2θw with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels qqˉ→qqˉ at tree level, including photon, gluon, W/Z, and Higgs exchange. Varying only αs, with all other inputs fixed at each center-of-mass energy, we find that the finite-αs magic minimum in the top channel reproduces the MS value of αs to within 5% from 1TeV to 109GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing αs toward α increases their magic production, potentially explaining why the strong interaction is ``strong.'' To understand why minimizing magic reproduces both sin2θw and αs, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.
The weak mixing angle sW is a fundamental constant in the Standard Model (SM) and measured at the Z boson mass to be sW2(mZ)=0.23129±0.00004 in the MS renormalization scheme, where mZ=91.2GeV. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the Z boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of sW2 in the Møller scattering e−e−→e−e−, which is free of kinematic thresholds. At the centre-of-mass energy s=mZ, there is a unique minimum in magic production at sW2(mZ)=0.2317, which agrees with the measured sW2(mZ) at the sub-percent level. At higher energies, the magic-minimizing sW2 continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.
The production of magic states is studied in two settings. The first is the electroweak (EW) sector of the Standard Model (SM). The second is an extension featuring a new broken U(1) gauge symmetry and a Dirac fermion charged under it. This setup resembles a dark U(1) scenario, with the additional fermion playing the role of a dark matter candidate that annihilates into SM particles through its coupling to the new gauge boson. In the EW sector, the low-energy regime reproduces earlier magic production results obtained for Quantum Electrodynamics, whereas the high-energy and Z-resonance regimes generate new magic distribution functions and non-trivially reorganize the stabilizer state classes, with Bhabha scattering exhibiting the strongest sensitivity to electroweak effects. Also, a subset of fixed stabilizer states is identified, for which the magic distributions remain unchanged across the different energy regimes. In the dark sector, the main effect of the new massive mediator is the appearance of new magic distributions functions for Moller-like, Bhabha-like, and inverse pair-annihilation processes in the low-energy limit. These reach the maximal magic value at the SM-to-dark fermion mass ratios mf/mχ→0 and mf/mχ→1.83929.
Magic, also known as non-stabilizerness, measures the usefulness of a quantum state for quantum computation. While magic is defined relative to a choice of computational basis, in some physical settings the available data determine this basis only up to local phase conventions. In this paper, we generalize the notion of magic and formulate it in a phase-independent manner, and hence define a generalized stabilizer Rényi entropy. As a case study, we consider higher-multiplicity tree-level gluon scattering, interpreting the outgoing helicities as qubits. In this setting, the helicity data naturally determine a local basis for each qubit but leave a phase ambiguity. For 3→2 scattering, we find that the final-state phase-independent magic is generically larger than the maximum attainable in 2→2 scattering. For 2→3 scattering, we find a nonzero minimal value approached in the soft limit. Moreover, when the three outgoing momenta become symmetric, the magic approaches a local minimum only a few percent above the soft-limit value. In all cases considered, the color dependence cancels from the phase-independent stabilizer Rényi entropy.