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Quantum discord in quantum random access codes and its connection to dimension witnesses

2012; American Physical Society; Volume: 86; Issue: 6 Linguagem: Inglês

10.1103/physreva.86.062310

1538-4446

Yao Yao, Hong-Wei Li, Xu‐Bo Zou, Jingzheng Huang, Chun-Mei Zhang, Zhen−Qiang Yin, Wei Chen, Guang−Can Guo, Zheng‐Fu Han,

Quantum Mechanics and Applications

We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in quantum information theory. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under some specific state rotations. In the two-state case, the connection between quantum discord and dimension witness is graphically discussed and intriguingly, our results illustrate that these two quantities are monotonically related to each other. For state encodings in the real $|0\ensuremath{\rangle}\ensuremath{-}|1\ensuremath{\rangle}$ plane, we derive an explicit analytical expression of the geometric discord and find that geometric discord reaches the maximal value for the optimal encoding strategy. However, for arbitrary state encodings in the Bloch sphere, our numerical simulations reveal that maximal geometric discord could not coincide with optimal $2\ensuremath{\rightarrow}1$ QRAC.