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arXiv · 2410.20023

Classifying coherence with a finite set of witnesses

Xue-Na Zhu·Zhi-Xiang Jin·Gui Bao·Shao-Ming Fei
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Abstract

Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. In order to detect all the coherent states, we introduce a useful concept of coherence witness and structure the set of coherence witnesses $C^{d}_{[m,M]}$. We present necessary and sufficient conditions of detecting quantum coherence of $d-$dimensional quantum states based on $C^{d}_{[m,M]}$. Moreover, we show that each coherent state can be detected by one of the coherence witnesses in a finite set. The corresponding finite set of coherence witnesses is presented explicitly, which detects all the coherent states.

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Xue-Na Zhu, Zhi-Xiang Jin, Gui Bao, Shao-Ming Fei. 2024-10-26. Classifying coherence with a finite set of witnesses. https://doi.org/10.1088/1751-8121%2Fad8795

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