Tractable measure of nonclassical correlation using density matrix truncations

  • Authors:

  • Akira Saitoh;Robabeh Rahimi;Mikio Nakahara

  • Affiliations:

  • Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and Engineering, Kinki University, Osaka, Japan 577-8502;Departments of Chemistry and Materials Science, Graduate School of Science, Osaka City University, Osaka, Japan 558-8585 and Institute for Quantum Computing, University of Waterloo, Waterloo, Cana ...;Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and Engineering, Kinki University, Osaka, Japan 577-8502 and Department of Physics, Kinki University, Osaka, Jap ...

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2011

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Abstract

In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of this paradigm, we propose a measure of nonclassical correlation by using truncations of a density matrix down to individual eigenspaces. It is computable within polynomial time in the dimension of the Hilbert space albeit imperfect in the detection range. This is in contrast to the measures conventionally used for the paradigm. The computational complexity and mathematical properties of the proposed measure are investigated in detail and the physical picture of its definition is discussed.