Linear optics for direct observation of quantum violation of pigeonhole principle by joint weak measurement

Abstract

When three pigeons are in two pigeonholes, at least two of them should be in the same pigeonhole, which is called pigeonhole principle. Recently Aharonov el al have shown that the principle can be violated in a pre-postselected quantum system. This violation sheds light on a new aspect of quantum correlations, as both of the pre and postselected states are separable states. To prove this kind of quantum correlations, a measurement apparatus must be arranged in entanglement to perform a joint measurement on the quantum system. In this paper we discuss how to design the state of entangled meters to achieve such a measurement. We also propose an experimental setup composed of linear optics for direct observation of violation of pigeonhole principle.