Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation

Authors:
Akira Saitoh;Robabeh Rahimi;Mikio Nakahara
Affiliations:
Quantum Information Science Theory Group, National Institute of Informatics, Tokyo, Japan and Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and Engineering, K ...;Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada;Research Center for Quantum Computing, Interdisciplinary, Graduate School of Science and Engineering, Kinki University, Higashi-Osaka, Osaka, Japan and Department of Physics, Kinki University, Hig ...
Venue:
Quantum Information & Computation
Year:
2012

Citing 2
Cited 0

Tractable measure of nonclassical correlation using density matrix truncations

Quantum Information Processing
Mathematical framework for detection and quantification of nonclassical correlation

Quantum Information & Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord implies the existence of nonclassical correlation. It is known that only the matrix transposition is nontrivial among Hermiticity-preserving (HP) linear EnCE maps when we use the changes in the eigenvalues of a density matrix due to a partial map for the purpose. In this paper, we prove that this is true even among not-necessarily HP (nnHP) linear EnCE maps. The proof utilizes a conventional theorem on linear preservers. This result imposes a strong limitation on the linear maps and promotes the importance of nonlinear maps.