Superdense coding of quantum states

We describe a method for nonobliviously communicating a 2l-qubit quantum state by physically transmitting l+o(l) qubits, and by consuming l ebits of entanglement plus some shared random bits. In the nonoblivious scenario, the sender has a classical description of the state to be communicated. Our method can be used to communicate states that are pure or entangled with the sender's system; l+o(l) and 3l+o(l) shared random bits are sufficient, respectively.