Optimizing classical communication in remote preparation of a general pure qubit

TL;DR

This paper presents an optimization method to minimize classical communication in remote pure qubit state preparation, using a geometric approach related to point arrangements on the Bloch sphere.

Contribution

It introduces a novel optimization procedure specifically for low-dimensional systems like qubits, addressing limitations of previous coding methods.

Findings

Optimization reduces classical communication cost for pure qubit preparation.

Geometric description via uniform point arrangements on the Bloch sphere.

Applicable to general pure qubit states, improving efficiency.

Abstract

How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.