Photons are the ideal carriers of quantum information for communication(1,2). Each photon can have a single or multiple qubits encoded in its internal quantum state, as defined by optical degrees of freedom such as polarization, wavelength, transverse modes and so on(3,4). However, as photons do not interact, multiplexing and demultiplexing the quantum information across photons has not been possible hitherto. Here, we introduce and demonstrate experimentally a physical process, named 'quantum joining', in which the two-dimensional quantum states (qubits) of two input photons are combined into a single output photon, within a four-dimensional Hilbert space. The inverse process is also proposed, in which the four-dimensional quantum state of a single photon is split into two photons, each carrying a qubit. Both processes can be iterated, and hence provide a flexible quantum interconnect to bridge multiparticle protocols of quantum information with multidegree-of-freedom ones, with possible applications in future quantum networking(5).