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The distribution of entangled states is a key task of utmost importance formany quantum information processing protocols. A commonly adopted setup fordistributing quantum states envisages the creation of the state in onelocation, which is then sent to (possibly different) distant receivers throughsome quantum channels. While it is undoubted and, perhaps, intuitively expectedthat the distribution of entangled quantum states is less efficient than thatof product states, a thorough quantification of this inefficiency (namely, ofthe difference between the quantum-state transfer fidelity for entangled andfactorized states) has not been performed. To this end, in this work, weconsider $n$-independent amplitude-damping channels, acting in parallel, i.e.,each, locally, on one part of an $n$-qubit state. We derive exact analyticalresults for the fidelity decrease, with respect to the case of product states,in the presence of entanglement in the initial state, for up to four qubits.Interestingly, we find that genuine multipartite entanglement has a moredetrimental effect on the fidelity than two-qubit entanglement. Our resultshint at the fact that, for larger $n$-qubit states, the difference in theaverage fidelity between product and entangled states increases with increasingsingle-qubit fidelity, thus making the latter a less trustworthy figure ofmerit.

Entangled States are Harder to Transfer than Product States