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arXiv:1006.2225 · Physical Review A

Demonstration of cluster-state shaping and quantum erasure for continuous variables

Yoshichika Miwa, Ryuji Ukai, Jun–ichi Yoshikawa, Radim Filip, Peter van Loock, Akira Furusawa

Published Sep 9, 2010• 22 citations
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Abstract

We demonstrate experimentally how to remove an arbitrary node from a continuous-variable cluster state and how to shorten any quantum wires of such a state. These two basic operations, performed in an unconditional fashion, are a manifestation of quantum erasure and can be employed to obtain various graph states from an initial cluster state. Starting with a sufficiently large cluster, the resulting graph states can then be used for universal quantum information processing. In the experiment, all variations of this cluster shaping are demonstrated on a four-mode linear cluster state through homodyne measurements and feedforward.

DOI
10.1103/physreva.82.032305

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We demonstrate experimentally how to remove an arbitrary node from a continuous-variable cluster state and how to shorten any quantum wires of such a state. These two basic operations, performed in an unconditional fashion, are a manifestation of quantum erasure and can be employed to obtain various graph states from an initial cluster state. Starting with a sufficiently large cluster, the resulting graph states can then be used for universal quantum information processing. In the experiment, all variations of this cluster shaping are demonstrated on a four-mode linear cluster state through homodyne measurements and feedforward.
One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.
Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.