Papers › Complexity of frustration: a new source of non-local non-stabilizerness
Complexity of frustration: a new source of non-local non-stabilizerness
J. Odavić, T. Haug, G. Torre, A. Hamma, F. Franchini, S. M. Giampaolo
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We advance the characterization of complexity in quantum many-body systems by examining W-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic" (measured as the Stabilizer R\'enyi Entropy -SRE-) that grows logarithmic with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with an extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a W-state, while in the rest of the phase to which the classic point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state's SRE is the sum of that of the W-states plus an extensive local contribution. Our work reveals that W-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.
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