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arXiv · 2508.03534

Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States

Lei-Yi-Nan Liu·Su Yi·Jian Cui
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Abstract

Magic, capturing the deviation of a quantum state from the stabilizer formalism, is a key resource underpinning the quantum advantage. The recently introduced stabilizer R\'enyi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods. We study SRE in translation-invariant matrix product states (MPS), deriving exact expressions for representative states and introducing a numerically stable algorithm, named bond-DMRG, to compute the SRE density in infinite systems. Applying this method, we obtain high-precision SRE densities for the ground state of the one-dimensional Ising model. We also analyze non-local SRE density, showing it is bounded by a universal function of entanglement entropy, and further prove that two-site mutual SRE vanishes asymptotically in injective MPS. Our work not only introduces a powerful method for extracting the SRE density in quantum many-body systems, but also numerically reveals a fundamental connection between magic and entanglement, thereby paving the way for deeper theoretical investigations into their interplay.

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Lei-Yi-Nan Liu, Su Yi, Jian Cui. 2025-08-05. Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States. https://doi.org/10.1103/7hzd-lv9k

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