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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.15300 |
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| _version_ | 1866910136127193088 |
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| author | Albot, Héloïse Paeckel, Sebastian |
| author_facet | Albot, Héloïse Paeckel, Sebastian |
| contents | A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the $σ$-ensembles $\unicode{x2013}$ a family of random quantum states with only a single control parameter. Crucially, these states are designed such that they can be tuned between volume-law and area-law behavior, which has been a major obstacle thus far. We construct representatives of this ensemble by imposing a probability distribution on the eigenvalues of the successive subsystems, and subsequently reconstructing a compatible global state using the matrix product state (MPS) formalism. Due to their area-law entanglement, our approach circumvents the intractability of Haar-random pure states in classical simulations of quantum systems and is more representative of typical Hamiltonian ground states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ensembles of random quantum states tunable from volume law to area law Albot, Héloïse Paeckel, Sebastian Quantum Physics Mathematical Physics A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the $σ$-ensembles $\unicode{x2013}$ a family of random quantum states with only a single control parameter. Crucially, these states are designed such that they can be tuned between volume-law and area-law behavior, which has been a major obstacle thus far. We construct representatives of this ensemble by imposing a probability distribution on the eigenvalues of the successive subsystems, and subsequently reconstructing a compatible global state using the matrix product state (MPS) formalism. Due to their area-law entanglement, our approach circumvents the intractability of Haar-random pure states in classical simulations of quantum systems and is more representative of typical Hamiltonian ground states. |
| title | Ensembles of random quantum states tunable from volume law to area law |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2604.15300 |