Magic phase transition and non-local complexity in generalized $W$ State

Abstract

We employ the Stabilizer Renyi Entropy (SRE) to characterize a quantum phase transition that has so far eluded any standard description and can thus now be explained in terms of the interplay between its non-stabilizer properties and entanglement. The transition under consideration separates a region with a unique ground state from one with a degenerate ground state manifold spanned by states with finite and opposite (intensive) momenta. We show that SRE has a jump at the crossing points, while the entanglement entropy remains continuous. Moreover, by leveraging on a Clifford circuit mapping, we connect the observed jump in SRE to that occurring between standard and generalized $W$-states with finite momenta. This mapping allows us to quantify the SRE discontinuity analytically.

8 pages including supplementary material, 3 figures

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• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Resource complexity of Symmetry Protected Topological phases
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing