Efficient Algorithms for All Port-Based Teleportation Protocols

Port-based teleportation (PBT) is a form of quantum teleportation in which no corrective unitary is required on the part of the receiver. Two primary regimes exist—deterministic PBT in which teleportation is always successful, but is imperfect, and probabilistic PBT, in which teleportation succeeds with probability less than one, but teleportation is perfect upon a success. Two further regimes exist within each of these, in which the resource state used for the teleportation is fixed to a maximally entangled state or free to be optimized. Recent works have resolved the long-standing problem of efficiently implementing port-based teleportation, tackling the two deterministic cases for qudits. Here, we provide algorithms in all four regimes for qubits. Emphasis is placed on the practicality of these algorithms, where we give polynomial improvements in the known gate complexity for PBT, as well as an exponential improvement in the required number of ancillas (albeit in separate protocols). Our approach to the implementation of the square-root measurement in PBT can be directly generalized to other highly symmetric state ensembles. For certain families of states, such a framework yields efficient algorithms in the case in which the Petz-recovery algorithm for the square-root measurement runs in exponential time. Published by the American Physical Society 2024