The typicality of symmetry-induced entanglement
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914508949159936 |
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| author | Boudreault, Christian Levasseur, Nicolas |
| author_facet | Boudreault, Christian Levasseur, Nicolas |
| contents | In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20786 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The typicality of symmetry-induced entanglement Boudreault, Christian Levasseur, Nicolas Quantum Physics Other Condensed Matter In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement. |
| title | The typicality of symmetry-induced entanglement |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2603.20786 |