A scheme for remote state preparation of a general pure qubit with optimized classical communication cost

How to use shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. Berry has given a constructive scheme for remotely preparing a general pure state, using a pure entangled state and finite classical communication. To optimize the classical communication cost, Berry employed a coding of the high-dimensional target state. Though working in the high-dimensional cases, the coding method is inapplicable for low-dimensional systems, such as a pure qubit. Since qubit plays a central role in quantum information theory, here we propose an optimization procedure which can be used to minimize the classical communication cost in preparing a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} points on the Bloch sphere, which provides a geometric description.