Exponential Quantum Tsallis Havrda Charvat Entropy of Type Alpha

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis Havrda Charvat entropy and discuss its some properties. Further, we gave the application of exponential Tsallis Havrda Charvat entropy in quantum information theory which is called exponential quantum Tsallis Havrda Charvat entropy with its some major properties such as non-negative, concavity and continuity. It is found that projective measurement will not decrease the quantum entropy of a quantum state and at the end of the paper gave an upper bound on the quantum exponential entropy in terms of ensembles of pure state.