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arXiv · 1902.02100

Quantum coherence in mutually unbiased bases

Yao-Kun Wang·Li-Zhu Ge·Yuan-Hong Tao
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Abstract

We investigate the $l_{1}$ norm of coherence of quantum states in mutually unbiased bases. We find that the sum of squared $l_{1}$ norm of coherence of the mixed state single qubit is less than two. We derive the $l_{1}$ norm of coherence of three classes of $X$ states in nontrivial mutually unbiased bases for $4$-dimensional Hilbert space is equal. We proposed "autotensor of mutually unbiased basis(AMUB)" by the tensor of mutually unbiased bases, and depict the level surface of constant the sum of the $l_{1}$ norm of coherence of Bell-diagonal states in AMUB. We find the $l_{1}$ norm of coherence of Werner states and isotropic states in AMUB is equal respectively.

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Yao-Kun Wang, Li-Zhu Ge, Yuan-Hong Tao. 2019-02-07. Quantum coherence in mutually unbiased bases. https://doi.org/10.1007/s11128-019-2283-9

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