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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2502.04437 |
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| _version_ | 1866910237423828992 |
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| author | Li, Zhi Mori, Takato Yoshida, Beni |
| author_facet | Li, Zhi Mori, Takato Yoshida, Beni |
| contents | We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net argument and concentration of measure. Viewing $|Ψ\rangle_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any non-trivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or GHZ-like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tripartite Haar random state has no bipartite entanglement Li, Zhi Mori, Takato Yoshida, Beni Quantum Physics High Energy Physics - Theory We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net argument and concentration of measure. Viewing $|Ψ\rangle_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any non-trivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or GHZ-like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief. |
| title | Tripartite Haar random state has no bipartite entanglement |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.04437 |