A hyper-entanglement based atmospheric imaging/detection system involving only a signal and an ancilla photon will be
considered for optical and infrared frequencies. Only the signal photon will propagate in the atmosphere and its loss will
be classical. The ancilla photon will remain within the sensor experiencing low loss. Closed form expressions for the
wave function, normalization, density operator, reduced density operator, symmetrized logarithmic derivative, quantum
Fisher information, quantum Cramer-Rao lower bound, coincidence probabilities, probability of detection, probability of
false alarm, probability of error after M measurements, signal to noise ratio, quantum Chernoff bound, time-on-target
expressions related to probability of error and resolution will be provided. The effect of noise in every mode will be
included as well as loss. The system will provide the basic design for an imaging/detection systems functioning at
optical or infrared frequencies that offer better than classical angular and range resolution. Optimization for enhanced
resolution will be included. The signal to noise ratio will be increased by a factor equal to the number of modes
employed during the hyper-entanglement process. Likewise, the measurement time can be reduced by the same factor.
The hyper-entanglement generator will typically make use of entanglement in polarization, energy-time, orbital angular
momentum, etc. Mathematical results will be provided describing the system’s performance as a function of loss
mechanisms and noise.