Exponential Tsallis-Havrda-Charvat Entropy and its Applications in Coding Theory, Industrial Engineering and Quantum Information Theory

In this paper, we define the exponential Tsallis-Havrda-Charvat entropy of ‘type Alpha ’ and discuss its some major properties corresponding to exponential Tsallis-Havrda-Charvat entropy of concave function. Further, we define the new measure of exponential relative information of ‘type Alpha ’ and discuss some special cases then present the new information measure when one of the probability distribution is uniform and gave the application of the function (4.1) and (4.9) in industrial engineering. Also, we define measure of length and show the relationship between the exponential Tsallis-Havrda-Charvat entropy E alpha (A) and average code word length, L alpha (A) . At the end of the paper, we gave the application of exponential Tsallis-Havrda-Charvat entropy for quantum information theory. It is found that projective measurement will not decrease the exponential entropy in terms of ensembles of pure state.