Understanding how entanglement can be reduced through simple operations is crucial for both classical and quantum algorithms. We investigate the entanglement properties of lattice models hosting conformal field theories cooled via local Clifford operations, a procedure we refer to as stabilizer disentangling. We uncover two distinct regimes: a constant gain regime, where disentangling is volume-independent, and a log-gain regime, where disentanglement increases with volume, characterized by a reduced effective central charge. In both cases, disentangling efficiency correlates with the target state magic, with larger magic leading to more effective cooling. The dichotomy between the two cases stems from mutual stabilizer Renyi entropy, which influences the entanglement cooling process. We provide an analytical understanding of such effect in the context of cluster Ising models, that feature disentangling global Clifford operations. Our findings indicate that matrix product states possess subclasses based on the relationship between entanglement and magic, and clarifying the potential of new classes of variational states embedding Clifford dynamics within matrix product states.
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List of changes
• We double-checked Arxiv references for updates, in particular, we updated Refs.[16,17,48,50,52] and the Note added paragraph • We added a DOI in Refs. [1-4,7-10,12,13,18-23,25,36,40,41,49,58] • We changed a paragraph in the introduction to clarify the summary of our main results, including a description of the connection between mχ=2 and the disentangling power. • We added a paragraph in Section 2.5 to motivate the choice of employing χ = 2 to measure the magic that cannot be removed by local operation.
