The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric

arXiv:2608.21437 · quant-ph, cond-mat.stat-mech, math-ph, math.MP · Submitted 2026-08-17 · Read on arXiv

quant-ph, cond-mat.stat-mech, math-ph, math.MP

Submitted: 2026-08-17

Updated: 2026-09-17

Comments: 26 pages, 3 figures, 1 table. Substantially revised and reorganized presentation; the main results and conclusions are unchanged. The revision clarifies the physical interpretation, the role of identical copies and real-amplitude readouts, the mixed-state information-loss mechanism, limitations, and relation to previous work

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fisher Information — 31× in this paper · explained in 3 episodes
• Entanglement — 8× in this paper · explained in 3 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Sample Complexity — 3× in this paper · explained in 15 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Additivity — 1× in this paper · explained in 1 episode
• Generalization — 1× in this paper · explained in 13 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Spectral Signature — 1× in this paper · explained in 2 episodes

Sources

• Hidden Conformal Boundary Data in Finite-Temperature Stabilizer Entropy
• Universal Crossovers of Stabilizer Entropy Beyond Criticality
• Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable R'enyi Indices
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Pauli Spectrum and Stabilizer R'enyi Entropy in Gapless Symmetry-Protected Topological Phases
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Nonstabilizerness via matrix product states in the Pauli basis
• Non-stabilizerness versus entanglement in matrix product states
• Learning stabilizer states by Bell sampling
• Bell sampling from quantum circuits
• Efficient quantum algorithms for stabilizer entropies
• Stabilizer R'enyi Entropy and Conformal Field Theory
• Conformal field theories are magical
• Stabilizer R'enyi entropy
• Many-body quantum magic
• Stabilizer disentangling of conformal field theories
• Nonstabilizerness in U(1) lattice gauge theory
• Stabilizer entropies and nonstabilizerness monotones

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