The problem is a security problem in a B92 quantum key distribution protocol, in which you have this scenario. You can atenuate the laser signal in order to emit single photon pulses with high probability, but there is a little probability of multiple photon emision. An eavesdropper can use the...
You can consider fixed N and that there are two possible polarization states, the question is more about the probability of the unambiguous measurement.
You can check "Unambiguous quantum measurement of nonorthogonal states", B. Huttner, A. Muller, J. D. Gautier, H. Zbinden, and N. Gisin...
Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...