Sequential Reattempt of Telecloning

TL;DR

This paper explores a telecloning protocol using unsharp measurements that allows resource recycling for up to three receivers, revealing limitations for more than three receivers and linking fidelity to entanglement measures.

Contribution

It introduces a sequential telecloning protocol with resource recycling, establishing the maximum number of rounds for quantum advantage and a no-go theorem for more than three receivers.

Findings

Maximum three rounds for two receivers with quantum advantage.

Recycling is not possible for more than three receivers.

Fidelity relates to bipartite entanglement and monogamy score.

Abstract

The task of a telecloning protocol is to send an arbitrary qubit possessed by a sender to multiple receivers. Instead of performing Bell measurement at the sender's node, if one applies unsharp measurement, we show that the shared state can be recycled for further telecloning protocol. Specifically, in case of a single sender and two receivers, the maximal attempting number, which is defined as the maximum number of rounds used by the channel to obtain quantum advantage in the fidelity, turns out to be three both for optimal and nonoptimal shared states for telecloning while the maximal number reduces to two in case of three receivers. Although the original telecloning with quantum advantage being possible for arbitrary numbers of receivers, we report that the recycling of resources is not possible in telecloning involving a single sender and more than three receivers, thereby demonstrating a no-go theorem. We also connect the maximal achievable fidelities in each round with the bipartite entanglement content of the reduced state between the sender and one of the receivers as well as with the monogamy score of entanglement.