This means that each photon can only take one of the two paths and can be detected by only one detector. As the path taken by each photon is a quantum process with probability 50%, each detection is completely random.
Therefore, the binary sequence generated via this process will be a random one.
Computer algorithms or any other deterministic method for the generation of random numbers are not truly random but pseudo-random processes, since knowing the generating algorithm will result in the determination of the whole sequence.
On the contrary, there are instances where it is fundamentally impossible to determine a priori the outcome of a measurement.
By quantum theory we know that after passing through the PBS the state of the system, either |V〉 or |H〉, is an eigenstate of the polarization operator.