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.

• Received 30 August 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.187901