Efficient methods for one-shot quantum communication

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.