Quantum teleportation implies symmetry-protected topological order
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917802804248576 |
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| author | Hong, Yifan Stephen, David T. Friedman, Aaron J. |
| author_facet | Hong, Yifan Stephen, David T. Friedman, Aaron J. |
| contents | We constrain a broad class of teleportation protocols using insights from locality. In the "standard" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a "resource state" exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $\mathcal{G}_{k}= (\mathbb{Z}_2 \times \mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_12227 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum teleportation implies symmetry-protected topological order Hong, Yifan Stephen, David T. Friedman, Aaron J. Quantum Physics Strongly Correlated Electrons Mathematical Physics We constrain a broad class of teleportation protocols using insights from locality. In the "standard" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a "resource state" exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $\mathcal{G}_{k}= (\mathbb{Z}_2 \times \mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state. |
| title | Quantum teleportation implies symmetry-protected topological order |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2310.12227 |