Stabilizer Entropies And Nonstabilizerness Monotones

Tobias Haug¹ and Lorenzo Piroli²

¹QOLS, Blackett Laboratory, Imperial College London SW7 2AZ, UK
²Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, F-75231 Paris, France

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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 Rényi index $0leq nleq2$, 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 $ngeq2$). Next, we show that, for any Rényi 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 Rényi 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.

► BibTeX data

@article{Haug2023stabilizerentropies, doi = {10.22331/q-2023-08-28-1092}, url = {https://doi.org/10.22331/q-2023-08-28-1092}, title = {Stabilizer entropies and nonstabilizerness monotones}, author = {Haug, Tobias and Piroli, Lorenzo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1092}, month = aug, year = {2023}<br /> }

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Cited by

[1] Poetri Sonya Tarabunga, Emanuele Tirrito, Titas Chanda, and Marcello Dalmonte, “Many-body magic via Pauli-Markov chains — from criticality to gauge theories”, arXiv:2305.18541, (2023).

[2] Emanuele Tirrito, Poetri Sonya Tarabunga, Gugliemo Lami, Titas Chanda, Lorenzo Leone, Salvatore F. E. Oliviero, Marcello Dalmonte, Mario Collura, and Alioscia Hamma, “Quantifying non-stabilizerness through entanglement spectrum flatness”, arXiv:2304.01175, (2023).

[3] Xhek Turkeshi, Marco Schirò, and Piotr Sierant, “Measuring Magic via Multifractal Flatness”, arXiv:2305.11797, (2023).

[4] Guglielmo Lami and Mario Collura, “Quantum Magic via Perfect Pauli Sampling of Matrix Product States”, arXiv:2303.05536, (2023).

[5] Junjie Chen, Yuxuan Yan, and You Zhou, “Magic of quantum hypergraph states”, arXiv:2308.01886, (2023).

[6] Oliver Hahn, Alessandro Ferraro, Lina Hultquist, Giulia Ferrini, and Laura García-Álvarez, “Erratum: Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [Phys. Rev. Lett. 128, 210502 (2022)]”, Physical Review Letters 131 4, 049901 (2023).

[7] Tobias Haug, Soovin Lee, and M. S. Kim, “Efficient stabilizer entropies for quantum computers”, arXiv:2305.19152, (2023).

[8] Davide Rattacaso, Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, “Stabilizer entropy dynamics after a quantum quench”, arXiv:2304.13768, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-08-28 14:10:25). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Stabilizer entropies and nonstabilizerness monotones

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