The maximum entropy principle discovered by Jaynes E T governs a search of the most reasonable probability assignment of stochastic variable,based on the measured data.One of the simplest applications of this principle lies in that all the thermodynamical relations are derived from the maximizing entropy of the system with energy as a single measured value.The maximum entropy principle is used then for the radiation field as a quantum system.Our results show that with an increase of the number of measurable quantities,the thermal field,the coherent states as well as the squeezed states are automatically introduced in turn;in particular,the dependence of all the properties of these radiation fields on the thermal noise is formulated quantitatively.The fundamental results obtained in this paper are expected to provide a basis for applications of the maximum entropy principle in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.
The recent article 'Entropic Updating of Probability and Density Matrices' [ 1 ] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative entropies are shown to be designed for the purpose of inferentially updating probability distributions and density matrices, respectively, when faced with incomplete information. We call the inferential updating procedure for density matrices the 'quantum maximum entropy method'. Standard inference techniques in probability theory can be criticized for lacking concrete physical consequences in physics; but here, because we are updating quantum mechanical density matrices, the quantum maximum entropy method has direct physical and experimental consequences. The present article gives a new derivation of the Quantum Bayes Rule, and some generalizations, using the quantum maximum entropy method while discuss some of the limitations the quantum maximum entropy method puts on the measurement process in Quantum Mechanics.
A fully self-consistent derivation of the Born rule is presented using an information-theoretic quantity called coherence cost, defined over candidate future frames in an observer-actualized time model. By applying the Maximum Entropy Principle with a constraint determined by inter-frame coherence, the theory naturally yields without invoking von Neumann entropy. This provides a mathematically clean and conceptually transparent origin for quantum probabilities within a discrete frame-based temporal structure.