Ideal deterministic quantum communication tasks require maximally entangled channels. The reality is that the maximally entangled channel is inevitably degraded to a non-maximally entangled one because of various decoherence mechanisms, seriously deteriorating the performance of quantum communication. Instead of adopting traditional entanglement purification or distillation to rebuild maximally entangled channels, we have designed a novel deterministic joint remote state preparation scheme using the degenerated non-maximally entangled state directly. A protocol for deterministic joint remote preparation of a two-dimensional quantum state via a non-maximally hyperentangled quantum channel has been devised with the help of auxiliary qudits. Then we generalize it to prepare a high-dimensional quantum state faithfully. No matter how weak the shared entanglement is, the success probability of communication is maintained at 100% as soon as it exists. This investigation provides an ideology for the construction of practical quantum communication networks.
