Quantum Probability Cancellation Due to a Single-Photon State

When an N-photon state enters a lossless symmetric beamsplitter from one input port, the photon distribution for the two output ports has the form of Bernouli Binormial, with highest probability at equal partition (N/2 at one outport and N/2 at the other). However, injection of a single photon state at the other input port can dramatically change the photon distribution at the outputs, resulting in zero probability at equal partition. Such a strong deviation from classical particle theory stems from quantum probability amplitude cancellation. The effect persists even if the N-photon state is replaced by an arbitrary state of light. A special case is the coherent state which corresponds to homodyne detection of a single photon state and can lead to the measurement of the wave function of a single photon state