# Structures of Three Types of Local Quantum Channels Based on Quantum Correlations

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## Abstract

In a bipartite quantum system, quantum states are classified as classically correlated (CC) and quantum correlated (QC) states, the later are important resources of quantum information and computation protocols. Since correlations of quantum states may vary under a quantum channel, it is necessary to explore the influence of quantum channels on correlations of quantum states. In this paper, we discuss CC-preserving, QC-breaking and strongly CC-preserving local quantum channels of the form \(\Phi _1\otimes \Phi _2\) and obtain the structures of these three types of local quantum channels. Moreover, we obtain a necessary and sufficient condition for a quantum state to be transformed into a CC state by a specific local channel \(\Phi _1\otimes \Phi _2\) in terms of the structure of the input quantum state. Lastly, as applications of the obtained results, we present a classification of local quantum channels \(\Phi _1\otimes \Phi _2\) and describe the quantum states which are transformed as CC ones by the corresponding local quantum channel.

## Keywords

Structure Local quantum channel Classical correlation Quantum correlation## Notes

### Acknowledgments

The authors would like to thank the referee for his/her kind comments and valuable suggestions. This research was partially supported by the National Natural Science Foundation of China (11401359, 11371012, 11301318, 11471200), China Postdoctoral Science Foundation (2014M552405), the Natural Science Research Program of Shaanxi Province (2014JQ1010) and Postdoctoral Science Foundation of Shaanxi Province.

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