Entanglement and Stabilizer entropies of random bipartite pure quantum states
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908458439147520 |
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| author | Iannotti, Daniele Esposito, Gianluca Venuti, Lorenzo Campos Hamma, Alioscia |
| author_facet | Iannotti, Daniele Esposito, Gianluca Venuti, Lorenzo Campos Hamma, Alioscia |
| contents | The interplay between non-stabilizerness and entanglement in random states is a very rich arena of study for the understanding of quantum advantage and complexity. In this work, we tackle the problem of such interplay in random pure quantum states. We show that while there is a strong dependence between entanglement and magic, they are, surprisingly, perfectly uncorrelated. We compute the expectation value of non-stabilizerness given the Schmidt spectrum (and thus entanglement). At a first approximation, entanglement determines the average magic on the Schmidt orbit. However, there is a finer structure in the average magic distinguishing different orbits where the flatness of entanglement spectrum is involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement and Stabilizer entropies of random bipartite pure quantum states Iannotti, Daniele Esposito, Gianluca Venuti, Lorenzo Campos Hamma, Alioscia Quantum Physics Mathematical Physics The interplay between non-stabilizerness and entanglement in random states is a very rich arena of study for the understanding of quantum advantage and complexity. In this work, we tackle the problem of such interplay in random pure quantum states. We show that while there is a strong dependence between entanglement and magic, they are, surprisingly, perfectly uncorrelated. We compute the expectation value of non-stabilizerness given the Schmidt spectrum (and thus entanglement). At a first approximation, entanglement determines the average magic on the Schmidt orbit. However, there is a finer structure in the average magic distinguishing different orbits where the flatness of entanglement spectrum is involved. |
| title | Entanglement and Stabilizer entropies of random bipartite pure quantum states |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2501.19261 |