Counterfactual Quantum Superdense Coding*

Quantum superdense coding (QSC) ) is one of the most striking effects in quantum communication. It enables one to transmit a two-bit classical message by sending only one qubit using initially shared entanglement. In this article, we present a counterfactual QSC scheme that enables remote parties to accomplish this task without prior entanglement but no physical particle is found in the transmission channel. We consider two remote parties, namely Alice (sender) and Bob (receiver), have untangled particles---an electron and a photon. First, we generate entanglement between the electron and photon without transmitting any physical particle over the channel. Alice performs one of the four unitary operations μ ∈ {Ι, σ_x, σ_Y, σ_Z } on her entangled particle. Instead of transmitting her entangled particle to Bob, Alice and Bob perform counterfactual Bell-state analysis based on the chained quantum Zeno effect to distinguish between the four Bell-states under local operations and enable Bob to decode the two-bit classical message.