Quantum teleportation implies symmetry-protected topological order

Journal Article · 10 October 2024 · Quantum

DOI: https://doi.org/10.22331/q-2024-10-10-1499 · OSTI ID:2462836

Hong, Yifan ^[1]; Stephen, David T. ^[2]; Friedman, Aaron J. ^[1]

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1. Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
2. Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA, Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0024324
• OSTI ID: 2462836
• Journal Information: Quantum, Journal Name: Quantum Vol. 8; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement
• Country of Publication: Austria
• Language: English