Nonlocality of tripartite orthogonal product states
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909744703209472 |
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| author | Bhunia, Atanu Chattopadhyay, Indrani Sarkar, Debasis |
| author_facet | Bhunia, Atanu Chattopadhyay, Indrani Sarkar, Debasis |
| contents | Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability found in bipartite quantum systems and very few are known in multipartite systems. In this work, we construct a locally indistinguishable subset in ${\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}$, $d\geq2$ that contains $18(d-1)$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems ${\mathbb{C}}^{k}\bigotimes{\mathbb{C}}^{l}\bigotimes{\mathbb{C}}^{m}$. This result enables us to understand further the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_03830 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nonlocality of tripartite orthogonal product states Bhunia, Atanu Chattopadhyay, Indrani Sarkar, Debasis Quantum Physics Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability found in bipartite quantum systems and very few are known in multipartite systems. In this work, we construct a locally indistinguishable subset in ${\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}$, $d\geq2$ that contains $18(d-1)$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems ${\mathbb{C}}^{k}\bigotimes{\mathbb{C}}^{l}\bigotimes{\mathbb{C}}^{m}$. This result enables us to understand further the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states. |
| title | Nonlocality of tripartite orthogonal product states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2011.03830 |