Marek Mozrzymas

Abstract We introduce and discuss a novel multi-port based teleportation schemes performing transmission of a number of unknown quantum states or one composite system in one go. We fully characterize the probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity in both non-optimal and optimal variant. We also deliver explicit forms of the measurements and the resource state exploited by parties to perform the process. To obtain our results, i.e. explicit expressions for the performance of the new schemes, we deliver novel mathematical tools concerning representation theory of the algebra of partially transposed permutation operators, where the transposition acts on more than one subsystem. Additionally, the optimal values of the entanglement fidelity and probability success emerge from formulated and solved primal and dual semidefinite problems, which due to existing symmetries and delivered mathematical tools could be solved analytically. Next, we have applied the obtained formulas for the performance of multi-port based teleportation schemes to get a qualitative improvement of asymptotic "teleportation capacities" of multi-port based teleportation schemes over the pre-existing port-based teleportation schemes.