Optimal Multi-port-based Teleportation Schemes

Abstract

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.

arXiv comment26 pages, 5 figures

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• Semidefinite programming relaxations for quantum correlations
• Multiport based teleportation -- transmission of a large amount of quantum information
• Optimality of the pretty good measurement for port-based teleportation
• Minimal Port-based Teleportation
• Linear programming with unitary-equivariant constraints
• Positive maps from the walled Brauer algebra
• Teleportation of Post-Selected Quantum States
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications
• Square-root measurements and degradation of the resource state in port-based teleportation scheme
• A resource theory of asynchronous quantum information processing