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Quantum teleportation implies symmetry-protected topological order
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 34 pages, 8 figures; v2 changes: added summary of main assumptions and results
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2310.12227
- Document Type :
- Working Paper