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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05036 |
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| _version_ | 1866917240001003520 |
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| author | Liu, Li |
| author_facet | Liu, Li |
| contents | We investigate the operator-algebraic structure underlying entanglement embezzlement, a phenomenon where a fixed entangled state (the catalyst) can be used to generate arbitrary target entangled states without being consumed. We show that the ability to embezzle a target state $g$ imposes strong internal constraints on the catalyst state $f$: specifically, $f$ must contain infinitely many mutually commuting, locally structured copies of $g$. This property is formalized using C*-algebraic tools and is analogous to a form of self-testing, certifying the presence of infinite copies of $g$ within $f$. Using this infinite-copy certification. Our results clarify the structural requirements for embezzlement and provide new conceptual tools for analyzing state certification in infinite-dimensional quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embezzlement as a "Self-Test" for Infinite Copies of Entangled States Liu, Li Quantum Physics We investigate the operator-algebraic structure underlying entanglement embezzlement, a phenomenon where a fixed entangled state (the catalyst) can be used to generate arbitrary target entangled states without being consumed. We show that the ability to embezzle a target state $g$ imposes strong internal constraints on the catalyst state $f$: specifically, $f$ must contain infinitely many mutually commuting, locally structured copies of $g$. This property is formalized using C*-algebraic tools and is analogous to a form of self-testing, certifying the presence of infinite copies of $g$ within $f$. Using this infinite-copy certification. Our results clarify the structural requirements for embezzlement and provide new conceptual tools for analyzing state certification in infinite-dimensional quantum systems. |
| title | Embezzlement as a "Self-Test" for Infinite Copies of Entangled States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.05036 |