Researchers have addressed the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding.
They introduced 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.
They showed 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, they constructed near-optimal communication protocol for quantum channel coding that uses exponentially smaller entanglement than the previous near-optimal protocol.
Anshu, A., Jain, R. Efficient methods for one-shot quantum communication. npj Quantum Inf 8, 97 (2022). https://doi.org/10.1038/s41534-022-00608-1
