Physics

Magic without a phase: phase-independent stabilizer Rényi entropy in gluon scattering

Jinwei Chu, Savan Kharel

Featured July 17, 2026

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Simply

By smoothing out arbitrary measurement quirks, scientists found a new way to measure "magic" in tiny particle collisions, showing how much useful quantum weirdness is truly there, no matter how you look at it.

In depth

The paper introduces a phase-independent stabilizer Rényi entropy (

f M_{q}

) to quantify "magic" (a resource for quantum computation) in quantum states, addressing the issue that standard magic measures depend on arbitrary local phase conventions. This is achieved by averaging the conventional stabilizer Rényi entropy over all possible local phase redefinitions of the qubit basis. The authors apply this generalized measure to gluon scattering amplitudes, demonstrating how the quantum states produced in high-energy collisions exhibit intrinsic magic independent of these phase ambiguities, and revealing new insights into their computational resource potential.

Key Takeaways

1
The paper defines a phase-independent stabilizer Rényi entropy ( $f M_{q}$ ) by averaging over local phase conventions, making magic a true invariant of the physical state when basis phases are ambiguous.
2
Applying this measure to gluon scattering amplitudes reveals that the "magic" of the resulting quantum states is fixed by kinematics alone, with color dependence canceling out.
3
The study shows that higher-multiplicity scattering (e.g., 3 $\to$ 2 gluons) can generate significantly more phase-independent magic than lower-multiplicity processes (e.g., 2 $\to$ 2 gluons), while adding more outgoing particles (e.g., 2 $\to$ 3 gluons) does not necessarily increase magic.

Conceptual Flow

HIGH LEVEL

Making Magic Measurement Consistent

The old way of measuring "magic" in quantum states changed depending on how you set up your measuring device, so they found a new way to average out those setup differences to get a true, consistent magic score.

Quantum State

Many Measurement Setups

Average Out Differences

Consistent Magic Score

Gluon Collisions Create Real Magic

When tiny gluons crash together, the new magic score shows that more complex crashes create more useful quantum weirdness, and this weirdness is always there, no matter the particle's color.

Simple Gluon Crash

Complex Gluon Crash

Measure Magic

Low Magic

High Magic