Abstract:

We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two methods for this; the first constructs a resource-efficient convex-split lemma and the second adapts the technique of classical correlated sampling in computer science literature. These lead to the following consequences in one-shot quantum information theory. First concerns the task of quantum decoupling, achieved in many previous works with the aid of a random or pseudo-random unitary. We show that given any choice of basis such as the computational basis, decoupling can be achieved by a unitary that takes basis vectors to basis vectors. Thus, the circuit acts in a ‘classical’ manner; furthermore our unitary performs addition and multiplication modulo a prime. As the second consequence, we construct near-optimal communication protocol for quantum channel coding that uses exponentially smaller entanglement than the previous near-optimal protocol.