Path superposition as resource for perfect quantum teleportation with separable states

TL;DR

This paper demonstrates that superposition of paths can enable perfect quantum teleportation with separable states, challenging the notion that entanglement is always necessary for quantum teleportation.

Contribution

It introduces superposition of paths as an alternative resource for quantum teleportation, allowing perfect teleportation with non-entangled states, unlike traditional protocols.

Findings

Superposition of paths enables perfect teleportation with separable states.

Superposition of indefinite causal order does not provide an advantage for pure product states.

Separable Werner states can also achieve quantum advantage with superposition of paths.

Abstract

Quantum teleportation is a quintessential quantum communication protocol that enables the transmission of an arbitrary quantum state between two distant parties without physically transmitting the state with the help of shared entanglement and limited classical communication. We show that it is possible to relax the entanglement requirement in quantum teleportation if we have access to a certain strain of superposition of quantum processes. Two types of superposition of quantum processes are generally considered in the literature: superposition of paths identified with quantum maps and superposition of indefinite causal orders of the maps. We find that when superposition of paths is incorporated in the protocol, perfect quantum teleportation becomes possible with nonzero probability, even when the two parties share certain classes of separable states, including pure product states. In contrast, the assistance of superposition of indefinite causal order of quantum maps in teleportation protocol does not enable any quantum advantage for shared pure product states. Furthermore, we show that separable Werner states can also yield quantum advantage in quantum teleportation assisted by the superposition of paths. Finally, we establish that the presence of quantum coherence in the control qubit is both necessary and sufficient to achieve quantum advantage in quantum teleportation assisted with superposition of paths. Our results highlight that while entanglement is a fundamental resource in standard quantum teleportation, superposition of paths can serve as an alternate resource for the same.