Despite being hard to manufacture in the real world, entanglement is abundant in Hilbert space. In fact, surprisingly large randomly chosen subspaces of a given bipartite quantum system will contain only near-maximally entangled states. I'll describe the intuition behind this result and a number of its consequences. These include a proof that the quantum identification capacity of 1 ebit is 2 qubits and a protocol for sending quantum states from Alice to Bob that achieves the same rates as the well-known "superdense coding" result: 2 qubits can be sent by physically transmitting only 1 qubit and consuming 1 ebit.
Based on joint work with Anura Abeyesinghe, Debbie Leung, Graeme Smith and Andreas Winter.