Constructing Four-Photon States for Quantum Communication and Information Processing

We provide a method for constructing a set of four-photon states suitable for quantum communication applications. Among these states is a set of concatenated quantum code states that span a decoherence-free subspace that is robust under collective-local as well as global dephasing noise. This method requires only the use of spontaneous parametric down-conversion, quantum state post-selection, and linear optics. In particular, we show how this method can be used to produce all sixteen elements of the second-order Bell gem \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{G}_{16}$\end{document} , which includes these codes states and is an orthonormal basis for the Hilbert space of four qubits composed entirely of states that are fully entangled under the four-tangle measure.