Entangled States are Harder to Transfer than Product States

TL;DR

This paper quantifies how entangled states are more difficult to transfer than product states in quantum channels, revealing that multipartite entanglement significantly reduces transfer fidelity, especially as system size grows.

Contribution

It provides exact analytical results on fidelity loss for entangled versus product states over amplitude-damping channels, highlighting the impact of multipartite entanglement.

Findings

Genuine multipartite entanglement reduces transfer fidelity more than two-qubit entanglement.

Fidelity difference between entangled and product states increases with system size and single-qubit fidelity.

For larger systems, entanglement makes state transfer less reliable.

Abstract

The distribution of entangled states is a key task of utmost importance for many quantum information processing protocols. A commonly adopted setup for distributing quantum states envisages the creation of the state in one location, which is then sent to (possibly different) distant receivers through some quantum channels. While it is undoubted and, perhaps, intuitively expected that the distribution of entangled quantum states is less efficient than that of product states, a thorough quantification of this inefficiency (namely, of the difference between the quantum-state transfer fidelity for entangled and factorized states) has not been performed. To this end, in this work, we consider $n$-independent amplitude-damping channels, acting in parallel, i.e., each, locally, on one part of an $n$-qubit state. We derive exact analytical results 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 more detrimental effect on the fidelity than two-qubit entanglement. Our results hint at the fact that, for larger $n$-qubit states, the difference in the average fidelity between product and entangled states increases with increasing single-qubit fidelity, thus making the latter a less trustworthy figure of merit.