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A. Re′nyi, “On the Notion of Entropy and Its Role in Probability Theory,” Proceedings of the forth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, Vol. 1, 1961, pp. 547-561.

has been cited by the following article:

• TITLE: A Comparative Study on Correlation Measures of Pure Bipartite States through Incomparability

  AUTHORS: Amit Bhar, Indrani Chattopadhyay, Debasis Sarkar

  KEYWORDS: LOCC; Entanglement; Incomparability

  JOURNAL NAME: Journal of Quantum Information Science, Vol.2 No.3, September 28, 2012

  ABSTRACT: The entanglement of a pure bipartite state is uniquely measured by the von-Neumann entropy of its reduced density matrices. Though it cannot specify all the non-local characteristics of pure entangled states. It was proven that for every possible value of entanglement of a bipartite system, there exists an infinite number of equally entangled pure states, not comparable(satisfies Nielsen’s criteria) to each other. In this work, we investigate other correlation measures of pure bipartite states that are able to differentiate the quantum correlations of the states with entropy of entanglement. In Schmidt rank 3, we consider the whole set of states having same entanglement and compare how minutely such states can be distinguished by other correlation measures. Then for different values of entanglement we compare the sets of states belonging to the same entanglement and also investigate the graphs of different correlation measures. We extend our search to Schmidt rank 4 and 5 also.