Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States

• URL: http://arxiv.org/abs/2508.03534v1
• Date: Tue, 05 Aug 2025 15:04:03 GMT
• Title: Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Authors: Lei-Yi-Nan Liu, Su Yi, Jian Cui,
• Abstract summary: R'enyi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods.<n>We numerically reveal a fundamental connection between magic and entanglement, thereby paving the way for deeper theoretical investigations into their interplay.
• Score: 2.930915232771767
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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