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In the case of quantum mechanics, expectation values for measurement outcomes correspond to probabilities, meaning that in the quantum mechanical formalism, individual measurement outcomes occur in a random manner.
Thus, we can use quantum processes as sources of true randomness for the generation of sequences of random numbers.
Since each detector has a time interval during which it must process the pulse, if during the same interval another photon arrives at the second detector, both will send a signal, which will be registered as a simultaneous detection.
In such a case, the corresponding entry in the random sequence must be discarded.
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.
In this work, the former is preferred since it is cheaper, easier to reproduce and can be easily accessed at the quantum optics laboratory at Universidad de los Andes.
To illustrate how quantum optics can be used to generate sequences of truly random numbers, let us consider an ensemble of photons prepared in the state where |V〉 stands for a photon in a vertically polarized quantum state and similarly |H〉 stands for a photon in a horizontally polarized quantum state.
It is possible that both detectors register a 1 and a 0 simultaneously.
Nonetheless, this has to do with the time resolution of the detectors, rather than with the quantum physics associated with the process.