在相互无偏基下基于Hellinger距离的相干性

Coherence Based on Hellinger Distance under Mutually Unbiased Basis

摘要: 本文研究了在相互无偏基下量子态的基于Hellinger距离的量子相干性，从中推导出在相互无偏基中对于三维X态存在不同的标准正交基下有相同的基于Hellinger距离的量子相干性。之后我们提出Bell对角态在三组“相互无偏的自张量基(autotensor of mutually unbiased basis (AMUB))”下的基于Hellinger距离的量子相干性，并且这三个相干值可以对f(x₁,x₂,x₃)中的未知数相互置换从而分别表示出来。我们还发现在四维Hilbert空间中的相互无偏基除AMUB外剩余两组基下Bell对角态的基于Hellinger距离的量子相干性是相同的。

Abstract: In this paper, we study the quantum coherence of quantum states based on Hellinger distance un-der mutually unbiased bases. We derive that there is the same quantum coherence based on Hellinger distance under different standard orthogonal bases for the three-dimensional X state in mutually unbiased bases. We propose the quantum coherence of Bell diagonal states based on Hellinger distance under three sets of “autotensor of mutually unbiased basis (AMUB)”, and these three coherence values can be permutated with each other to represent the unknowns in f(x₁,x₂,x₃) . We also find that the quantum coherence of Bell-diagonal states based on Hellinger distance is the same under the two sets of mutually unbiased bases except AMUB in the four-di- mensional Hilbert space.