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

Amit Bhar, Indrani Chattopadhyay, Debasis Sarkar

Department of Applied Mathematics, University of Calcutta, Kolkata, India.
Department of Mathematics, Jogesh Chandra Chaudhuri College, Kolkata, India.

DOI: 10.4236/jqis.2012.23015                

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.

Keywords

LOCC; Entanglement; Incomparability

Conflicts of Interest

The authors declare no conflicts of interest.

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