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arXiv:quant-ph/0509057 · Journal of Optics B Quantum and Semiclassical Optics

Remote implementation of quantum operations

Susana F. Huelga, Martin Bodo Plenio, Guo‐Yong Xiang, Jian Li, Guang‐Can Guo

Published Sep 21, 2005• 29 citations
arXivHTMLPDF

Abstract

Shared entanglement allows, under certain conditions, the remote implementation of quantum operations. We revise and extend recent theoretical results on the remote control of quantum systems as well as experimental results on the remote manipulation of photonic qubits via linear optical elements.
DOI
10.1088/1464-4266/7/10/026

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We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as quantum remote control. We investigate protocols that achieve this using local operations, classical communication, and shared entanglement. Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
Quantum remote control, also known as quantum remote implementation of an operator (QRIO), enables the remote manipulation of an arbitrary quantum state by implementing a desired quantum operation at a distant location. Significant progress has recently been made in developing QRIO protocols and their variants. Most existing schemes employ hyperentangled states where entanglement is shared across multiple degrees of freedom (DOFs). However, these protocols typically exploit only one degree of freedom at a time. In this work, we propose a QRIO protocol that simultaneously utilizes the polarization and spatial DOFs of a two-qubit hyperentangled state to remotely implement an arbitrary hybrid operator on an unknown single-photon two-qubit hyperstate. The shared hyperentangled resource is realized using the polarization and spatial modes of photons, while the protocol is constructed using linear optical elements and cross-Kerr nonlinear interactions to facilitate effective photon-photon coupling. Furthermore, the effects of measurement errors arising from finite coherent state distinguishability and coherent state dissipation are analyzed and the corresponding success probability of the protocol is evaluated. The results demonstrate that an appropriate choice of the cross-Kerr phase shift and coherent state amplitude significantly enhances the protocol performance, making the proposed scheme a promising candidate for hybrid quantum communication and distributed quantum information processing.