Critical behaviors of non-stabilizerness in quantum spin chains
The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| Published: | 2024-07-17, volume 8, page 1413 |
| Eprint: | arXiv:2309.00676v3 |
| Doi: | https://doi.org/10.22331/q-2024-07-17-1413 |
| Citation: | Quantum 8, 1413 (2024). |
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Abstract
Non-stabilizerness – commonly known as magic – measures the extent to which a quantum state deviates from stabilizer states and is a fundamental resource for achieving universal quantum computation. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains. To quantify non-stabilizerness, we employ a monotone called mana, based on the negativity of the discrete Wigner function. This measure captures non-stabilizerness for both pure and mixed states. We introduce Rényi generalizations of mana, which are also measures of non-stabilizerness for pure states, and utilize it to compute mana in large quantum systems. We consider the three-state Potts model and its non-integrable extension and we provide strong evidence that the mutual mana exhibits universal logarithmic scaling with distance in conformal field theory, as is the case for entanglement.
Popular summary
Recent advancements have focused on a measure of magic called stabilizer entropies (SEs), that however have some limitations. In this work, we show how to compute a different measure called mana, which goes beyond SEs. Utilizing this, we study mana around phase transitions in quantum spin chains, offering new insights into the connection between magic and criticality in quantum systems.
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