  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.
