Multicopy quantum state teleportation with application to storage and retrieval of quantum programs

TL;DR

This paper introduces a probabilistic multicopy quantum state teleportation protocol for scenarios where Bob cannot perform corrections, and demonstrates its application to improving quantum program storage and retrieval.

Contribution

It provides a new multicopy teleportation protocol with a proven success probability and applies it to enhance quantum program storage and retrieval methods.

Findings

Success probability for exact state teleportation: p(d,k)=k/[d(k-1+d)]

Explicit protocol achieving the maximal success probability

Application of multicopy teleportation to quantum program storage and retrieval

Abstract

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of \textit{multicopy state teleportation}, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.