Linear-optical four-dimensional Bell state measurement for superdense coding assisted by polarization entanglement

With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.