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Stabilizer entropies and nonstabilizerness monotones
- Source :
- Quantum 7, 1092 (2023)
- Publication Year :
- 2023
-
Abstract
- We study different aspects of the stabilizer entropies (SEs) and compare them against known nonstabilizerness monotones such as the min-relative entropy and the robustness of magic. First, by means of explicit examples, we show that, for R\'enyi index $0\leq n<2$, the SEs are not monotones with respect to stabilizer protocols which include computational-basis measurements, not even when restricting to pure states (while the question remains open for $n\geq 2$). Next, we show that, for any R\'enyi index, the SEs do not satisfy a strong monotonicity condition with respect to computational-basis measurements. We further study SEs in different classes of many-body states. We compare the SEs with other measures, either proving or providing numerical evidence for inequalities between them. Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. In addition to previously developed exact methods to compute the R\'enyi SEs, we also put forward a scheme based on perfect MPS sampling, allowing us to compute efficiently the von Neumann SE for large bond dimensions.<br />Comment: 14 pages, 5 figures
- Subjects :
- Quantum Physics
Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Journal :
- Quantum 7, 1092 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2303.10152
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.22331/q-2023-08-28-1092