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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2406.16827 |
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| _version_ | 1866910499847798784 |
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| author | Jones, Benjamin D. M. Montanaro, Ashley |
| author_facet | Jones, Benjamin D. M. Montanaro, Ashley |
| contents | We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has this property or is $ε$-far in trace distance from any state with this property. We show that $Ω(n / \log n)$ copies are required (for fixed $ε\leq \frac{1}{2}$), complementing a previous result that $O(n / ε^2)$ copies are sufficient. Our proof technique proceeds by considering uniformly random ensembles over such states, and showing that the trace distance between these ensembles becomes arbitrarily small for sufficiently large $n$ unless the number of copies is at least $Ω(n / \log n)$. We discuss implications for testing graph states and computing the generalised geometric measure of entanglement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing multipartite productness is easier than testing bipartite productness Jones, Benjamin D. M. Montanaro, Ashley Quantum Physics We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has this property or is $ε$-far in trace distance from any state with this property. We show that $Ω(n / \log n)$ copies are required (for fixed $ε\leq \frac{1}{2}$), complementing a previous result that $O(n / ε^2)$ copies are sufficient. Our proof technique proceeds by considering uniformly random ensembles over such states, and showing that the trace distance between these ensembles becomes arbitrarily small for sufficiently large $n$ unless the number of copies is at least $Ω(n / \log n)$. We discuss implications for testing graph states and computing the generalised geometric measure of entanglement. |
| title | Testing multipartite productness is easier than testing bipartite productness |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.16827 |