Maximum efficiency of general two qubit linear-optical state analyzers

Linear optics is a critical technology for quantum information due to its reliability and ease of implementation. However, despite these advantages, linear optics is hampered by the limited set of total possible operations that can be performed with linear optical setups. While it has been shown that any general transformation can be performed on a optical system using only linear optics, these setups only succeed with some probability. In general, determining the optimal approach to implementing a linear optical operation is an extremely non-trivial task. In this paper, we specifically focus on the problem of measuring two qubit states in an arbitrary basis. For entangled basis states, such as the Bell-states, a perfect state analyzer is impossible. When we restrict our analysis to not allowing any auxiliary photons to be used in the discrimination process, we are able to derive that it is not possible to discriminate unambiguously any arbitrary basis of entangled two-qubit states with a probability higher than 50%. This is a generalization upon the previously known only for the Bell basis. Additionally, we specifically consider how to achieve the optimal unambiguous discrimination of bell-like states. We derive a general method for discriminating between bell-like states with a success rate of 25%.