Tight and self-testing multipartite quantum Bell inequalities from the renormalization group
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910860005343232 |
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| author | Abiuso, Paolo Fischer, Julian Navascués, Miguel |
| author_facet | Abiuso, Paolo Fischer, Julian Navascués, Miguel |
| contents | In past work, the concept of connectors was introduced: directed tensors with the property that any contraction thereof defines a multipartite quantum Bell inequality, i.e., a linear restriction on measurement probabilities that holds in any multipartite quantum experiment. In this paper we propose the notion of ''tight connectors'', which, if contracted according to some simple rules, result in tight quantum Bell inequalities. By construction, the new inequalities are saturated by tensor network states, whose structure mimics the corresponding network of connectors. Some tight connectors are furthermore ''fully self-testing'', which implies that the quantum Bell inequalities they generate can only be maximized with such a tensor network state and specific measurement operators (modulo local isometries). We provide large analytic families of tight, fully self-testing connectors that generate $N$-partite quantum Bell inequalities of correlator form for which the ratio between the maximum quantum and classical values increases exponentially with $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight and self-testing multipartite quantum Bell inequalities from the renormalization group Abiuso, Paolo Fischer, Julian Navascués, Miguel Quantum Physics In past work, the concept of connectors was introduced: directed tensors with the property that any contraction thereof defines a multipartite quantum Bell inequality, i.e., a linear restriction on measurement probabilities that holds in any multipartite quantum experiment. In this paper we propose the notion of ''tight connectors'', which, if contracted according to some simple rules, result in tight quantum Bell inequalities. By construction, the new inequalities are saturated by tensor network states, whose structure mimics the corresponding network of connectors. Some tight connectors are furthermore ''fully self-testing'', which implies that the quantum Bell inequalities they generate can only be maximized with such a tensor network state and specific measurement operators (modulo local isometries). We provide large analytic families of tight, fully self-testing connectors that generate $N$-partite quantum Bell inequalities of correlator form for which the ratio between the maximum quantum and classical values increases exponentially with $N$. |
| title | Tight and self-testing multipartite quantum Bell inequalities from the renormalization group |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.03878 |