Weak entanglement improves quantum communication using only passive linear optics

We show that noisy entangled states, that cannot violate any Bell inequality, can be used to improve quantum communication when measurements are limited to being compatible with standard, ancilla-free, linear optics. We introduce a communication task inspired by the cryptographic primitive known as secret sharing and show that entanglement that is too weak to permit possible Einstein-Podolsky-Rosen steering can still enhance the success rate when using only standard partial Bell state analysers for decoding. We then go further and show that even the simplest type of decoding, namely product measurements, which require no optical interference at all, can still lead to an advantage when the entanglement is steerable but still Bell-local. We demonstrate the former advantage by preparing polarisation qubits in an unsteerable entangled state and by using only beam-splitters and phase-shifters observing a boost in the success rate of beyond the best entanglement-unassisted qubit protocol.