Optimal probabilistic storage and retrieval of unitary channels

TL;DR

This paper presents an optimal probabilistic protocol for storing and retrieving unknown unitary channels in quantum systems, significantly reducing the required memory size and advancing quantum information processing capabilities.

Contribution

It introduces a new optimal protocol for probabilistic storage and retrieval of unitary channels, improving memory size efficiency and success probability over previous methods.

Findings

Success probability of perfect retrieval is N/(N-1+d^2)

Memory size exponentially smaller than previous bounds

Results relate to probabilistic reference frame alignment and teleportation

Abstract

We address the question of a quantum memory storage of quantum dynamics. In particular, we design an optimal protocol for $N\to 1$ probabilistic storage-and-retrieval of unitary channels on $d$-dimensional quantum systems. If we may access the unknown unitary gate only $N$-times, the optimal success probability of perfect retrieval of its single use is $N/(N-1+d^2)$. The derived size of the memory system exponentially improves the known upper bound on the size of the program register needed for probabilistic programmable quantum processors. Our results are closely related to probabilistic perfect alignment of reference frames and probabilistic port-based teleportation.