What Is "Quantum Magic"?

What does the term quantum magic, when used in a quantum physics scientific context (for example, in this preprint) mean?

"When you throw something into a black hole, information about it gets scrambled and cannot be recovered," says Goto. "This scrambling is a manifestation of chaos."

The team came across "magic," which is a mathematical measure of how difficult a quantum state is to simulate using an ordinary classical (non-quantum) computer. Their calculations showed that in a chaotic system almost any state will evolve into one that is "maximally magical"—the most difficult to simulate.

This provides the first direct link between the quantum property of magic and the chaotic nature of black holes. "This finding suggests that magic is strongly involved in the emergence of spacetime," says Goto.

From Phys.org discussing Kanato Goto et al, Probing chaos by magic monotones, Physical Review D (2022). DOI: 10.1103/PhysRevD.106.126009

Thus, "quantum magic" is simply an evocative name for a scientifically well-defined, but somewhat technical and obscure concept related to the difficulty of doing quantum physics calculations in a particular situation. 

This emergent descriptive property would naively just be a degree of difficulty factor useful for nothing more than estimating how much work will be involved in doing the calculations. It seems, surprisingly however, to have real world physical relevance in a manner somewhat analogous to the usual concept of "entropy" which was originally developed in the physics associated with thermodynamics. Indeed, as the preprint below operationalizes the concept, it is actually a very particularly defined kind of entropy (as distinct from the ordinary plain vanilla kind that is implied when the term entropy is used without any qualifiers or specifiers).

The preprint linked above and its abstract are as follows:

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for N(ν)≤8 neutrinos. 

For |ν(e)⟩^⊗N(ν) initial states, the magic, as measured by the α=2 stabilizer Renyi entropy M(2), is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. 

Further, the asymptotic magic per neutrino, M(2)/N(ν), decreases with increasing N(ν). In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic M(2)/N(ν) increasing with N(ν). 

These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

Ivan Chernyshev, Caroline E. P. Robin, Martin J. Savage, "Quantum Magic and Computational Complexity in the Neutrino Sector" arXiv:2411.04203 (November 6, 2024).

The term "qutrit" (a.k.a. or quantum trit) mentioned in the preprint's abstract, in turn, "is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states."

The downside of the term "quantum magic", however, is that the phrase is also used in a variety of contexts where its narrow quantum physics definition is not the intended meaning.