Authors: Koji Nagata, Do Ngoc Diep, Tadao Nakamura
We study the mathematical foundations of quantum optics. We consider the case that the ncertainty principle exists because we think both of commutativeness and non-commutativeness and then we derive natural value. On the other hand, we consider the case that the uncertainty principle does not exist because we think only commutativeness and then we derive unnatural value. We propose an experimental accessible inconsistency within quantum optical phenomenain terms of imperfect sources and detectors.In more detail, we encounter an imperfect quantum state, the dark count, and the quantum efficiency, which cannot be avoidable in a real experimental situation. Such an error of the number of particles becomes less and less important as we increase trials more and more by using the strong law of large numbers.As a result of our study, a perfect mathematical model for quantum optical phenomena does not exist, at this stage.
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