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Quantum discord of states arising from graphs

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Abstract

Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works, we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one-to-one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties, we define graph theoretic measures for normality and commutativity that results in a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the developed formulation.

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Acknowledgements

This work was partially supported by the Project Graph theoretical aspects in quantum information processing [Grant No. 25(0210)/13/EMR-II] funded by Council of Scientific and Industrial Research, New Delhi. S.D. is grateful to the Ministry of Human Resource Development, Government of India, for a doctoral fellowship. This work may be a part of his doctoral thesis.

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Authors and Affiliations

  1. Department of Mathematics, IIT Jodhpur, Jodhpur, India

    Supriyo Dutta

  2. Department of Mathematics, IIT Kharagpur, Kharagpur, India

    Bibhas Adhikari

  3. Department of Physics, IIT Jodhpur, Jodhpur, India

    Subhashish Banerjee

Authors
  1. Supriyo Dutta
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  2. Bibhas Adhikari
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  3. Subhashish Banerjee
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Corresponding author

Correspondence to Supriyo Dutta.

Additional information

This work is supported by CSIR (Council of Scientific and Industrial Research) Grant No. 25(0210)/13/EMR-II, New Delhi, India.

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Dutta, S., Adhikari, B. & Banerjee, S. Quantum discord of states arising from graphs. Quantum Inf Process 16, 183 (2017). https://doi.org/10.1007/s11128-017-1636-5

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