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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10561 |
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| _version_ | 1866910288127721472 |
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| author | Liu, Zhuohao Johnson, Emma C. Feder, David L. |
| author_facet | Liu, Zhuohao Johnson, Emma C. Feder, David L. |
| contents | All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10561 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation Liu, Zhuohao Johnson, Emma C. Feder, David L. Quantum Physics All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit but which is unable to deterministically teleport a universal set of single-qubit gates. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry. |
| title | Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.10561 |