Dr P. Kopszak (University of Wrocław): Multi port-based teleportation — a group theoretic approach

Dr Piotr Kopszak (University of Wrocław).
Multi port-based teleportation - a group theoretic approach.
Quantum teleportation, employing shared entangled resource, quantum measurement on the sender's side together with classical communication and unitary correction on the receiver's side is one of the most important examles of the usage of quantum entanglement in quantum information theory. However, the presece of the unitary correction in the last step is sometimes a limiting factor. This step was removed in so-called port-based teleportatio (PBT), in which two parties share not one, but N enatangled pairs. It turns out that in the asymptotic limit of the size of the shared resource, faithful teleportation of a qudit state is possible. In my presentation I am goning to answer the question what is the capability of PBT protocols to teleport multiple (i.e k) qudit states. Due to the symmetries present in the problem, its decripion will require the study of the commutant of U^(n-k) ⊗ U*^k transformations, where U belongs to the unitary group U(d), which heavcily relies on the results regarding the representation theory of the symmetric group.
Quantum Information and Quantum Computing Seminars CTP PAS
2023-05-10