Graphical description of local Gaussian operations for continuous-variable weighted graph states

Abstract

The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The novel property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which can not be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.

5 pages, 6 figures

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• Gaussian Quantum Information
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• Quantum Communication Network Utilizing Quadripartite Entangled States of Optical Field
• Hidden qubit cluster states
• Physical Realization of Measurement Based Quantum Computation
• Continuous-variable multipartite unlockable bound entangled Gaussian states
• Sequential measurement-based quantum computing with memories
• Graphical rule of transforming continuous-variable graph states by local homodyne detection
• Scheme for constructing graphs associated with stabilizer quantum codes
• Flow conditions for continuous variable measurement-based quantum computing
• Graphical Framework for Non-Gaussian Quantum States
• Optical Quantum Computing