How to upload a physical state to the correlation space

TL;DR

This paper explores how to upload a quantum state from physical space to the correlation space in tensor network frameworks, proposing a teleportation-like method and discussing its advantages over previous approaches.

Contribution

It introduces a novel teleportation-like method for uploading states to the correlation space, enabling hybrid quantum information processing.

Findings

Proves impossibility of cloning between physical and correlation spaces.

Proposes a teleportation-like upload method.

Demonstrates applications like gate teleportation and entanglement swapping.

Abstract

In the framework of the computational tensor network [D. Gross and J. Eisert, Phys. Rev. Lett. {\bf98}, 220503 (2007)], the quantum computation is performed in a virtual linear space which is called the correlation space. It was recently shown [J. M. Cai, W, D\"ur, M. Van den Nest, A. Miyake, and H. J. Briegel, Phys. Rev. Lett. {\bf103}, 050503 (2009)] that a state in the correlation space can be downloaded to the real physical space. In this letter, conversely, we study how to upload a state from a real physical space to the correlation space being motivated by the virtual-real hybrid quantum information processing. After showing the impossibility of the cloning of a state between the real physical space and the correlation space, we propose a simple teleportation-like method of the upload. Applications of this method also enable the Gottesman-Chuang gate teleportation trick and the entanglement swapping in the virtual-real hybrid setting. Furthermore, compared with the inverse of the downloading method by Cai, et. al., which also works as the upload, our uploading method has several advantages.