Network coding for quantum cooperative multicast

Cooperative communication is starting to attract substantial research attention in quantum information theory. However, given a specific network, it is still unknown whether quantum cooperative communication can be successfully performed. In this paper, we investigate network coding for quantum cooperative multicast (QCM) over the classic butterfly network. A very reasonable definition of QCM is first introduced. It not only perfectly focuses on the basic idea of quantum cooperative communication, but also wonderfully reflects the characteristic of classical multicast over a specific network structure. Next, we design QCM protocol for two-level systems and generalize the protocol into d-dimensional Hilbert space. It is shown that our protocols have significant advantages in terms of resource cost and compatibility with classical multicast. Besides, the success probability, which only depends on the coefficients of the initial quantum states, is carefully analyzed. In particular if the source nodes choose the quantum equatorial states, success probability can reach 1.