Optimal Multi-port-based Teleportation Schemes

Marek Mozrzymas1, Michał Studziński2, and Piotr Kopszak1

1Institute for Theoretical Physics, University of Wrocław, 50-204 Wrocław, Poland
2Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, University of Gdańsk, 80-952 Gdańsk, Poland

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In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports $N$, the number of teleported systems $k$, and local dimension $d$. It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number $N$ of ports increases as $o(N)$ still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.

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Cited by

[1] Piotr Kopszak, Marek Mozrzymas, Michał Studziński, and Michał Horodecki, "Multiport based teleportation -- transmission of a large amount of quantum information", arXiv:2008.00856.

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