[Un]known Information in Quantum Uncertainty

Wonmin Son (Sogang University)
 
Uncertainty principle is at the heart of basic construction of quantum mechanics. Contrary to the
 common textbook formulation, there is more than single way to express quantum uncertainty
 relation. It is because the concept of uncertainty is quite abstract to be quantified. Uncertainty, as
 an incompleteness of knowledge, can be characterized based upon the standard deviation of a
 statistical distribution or the information characterized by entropy. However, it is not yet clear
 which quantification of the quantum uncertainty is superior in various situations. In this talk, we
 review the historical trajectory of the formulation of quantum uncertainty principle and provide
 quantitative comparison between them. Knowing that the whole formalism of quantum optics is
 based upon the Heisenberg uncertainty relation, it is interesting to identify how much the
 description of quantum state of light is viewed differently in the framework of quantum uncertainty
 defined by Shannon¡¯s entropy.