The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity

Understand

Entanglement-assisted classical communication and transmission of a quantum system are the two quantum resources for information processing.

• Many information tasks can be performed using either quantum resource.
• However, this equivalence is not always present since entanglement assisted classical communication is known to sometimes be the better performing resource.
• Here, we show not only the opposite phenomenon; that there exists tasks for which transmission of a quantum system is a more powerful resource than entanglement assisted classical communication, but also that such phenomena can have a surprisingly strong dependence on the dimension of Hilbert space.