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Conformal field theories are magical
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abstract
"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the $\mathbb Z_3$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q = 3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.
Forward citations
Cited by 7 Pith papers
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Universality of Magic in Local Quantum Field Theory
In any local QFT, vacuum-like states have non-flat entanglement spectra because local algebras are type III₁, so no stabilizer state can flow to them in the continuum: QFT states necessarily carry magic.
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Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
For chaotic all-to-all systems, the stabilizer Rényi entropy of thermofield double states is set by the spectral form factor and saturates through a first-order dynamical transition.
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Nonlocal Nonstabilizerness from Holographic Schwinger Pair Production
In holographic Schwinger pair production, the excess capacity of entanglement is √λ(d−2)/(d−1)³ — positive for d>2, zero for d=2 — so the produced pair carries nonlocal magic for d>2.
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Experimental characterization of the hierarchy of quantum correlations in top quark pairs
LHC top-quark data show quantum discord at >5σ, first evidence for steering at >3σ, no Bell correlations, and nonzero magic.
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On the stabilizer complexity of Hawking radiation
In the PSSY model, the Wigner negativity (stabilizer magic) of Hawking radiation is O(1) before the Page time and grows as sqrt(2/pi) exp((S_max - S_2)/2) afterward; a similar formula is proposed for holographic state...
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Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness
Imposing magic conservation, equivalent to commutativity of the initial density matrix and the T-matrix, in 2-to-2 two-Higgs-doublet scattering yields SO(8) for arbitrary initial states and SU(2)_R for definite-isospi...
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Delay-Independent Stability of Nonlinear Delay Differential Equations via Isospectral Reduction
Claims a delay-independent global exponential stability criterion for a broad class of nonlinear nonautonomous delay differential equations using isospectral reduction of an associated sequence of matrices.
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