Daniele Iannotti

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The Haar measure provides a rigorous framework for characterizing uniform randomness in quantum states and unitary evolutions, serving as a benchmark for state-dependent quantities such as entanglement, coherence, and non-stabilizerness (magic). We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as a primary measure, we derive the exact average and variance for U(1)-constrained Haar random states across different charge sectors. We demonstrate that the presence of a conserved charge leads to a substantial suppression of magic compared to unconstrained random states. Furthermore, we identify a qualitative difference in the thermodynamic limit: stabilizer entropy exhibits a leading-order scaling near vanishing charge densities that makes it more robust to charge density fluctuations than entanglement entropy. We validate our analytical predictions against the midspectrum eigenstates of two paradigmatic chaotic systems: the non-local complex-fermion Sachdev-Ye-Kitaev (cSYK) model and a local Heisenberg XXZ chain with next-to-nearest-neighbor couplings. Our findings show excellent agreement for the non-local cSYK model, while systematic deviations in the local XXZ chain highlight the fundamental role of local interactions in shaping the complexity of physical eigenstates. These results reveal that stabilizer entropy is a sensitive probe for uncovering how global conservation laws and locality fundamentally reshape the landscape of quantum complexity.

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Scuola Superiore Meridionale, Naples
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Contact: Markus Heinrich