Complete Analysis of Four-Photon χ-Type Entangled State via Cross-Kerr Nonlinearity

We propose an efficient method to construct an optical four-photon |χ state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ state.