Classifying coherence with a finite set of witnesses

• URL: http://arxiv.org/abs/2410.20023v1
• Date: Sat, 26 Oct 2024 00:44:49 GMT
• Title: Classifying coherence with a finite set of witnesses
• Authors: Xue-Na Zhu, Zhi-Xiang Jin, Gui Bao, Shao-Ming Fei,
• Abstract summary: Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. We present necessary and sufficient conditions of detecting quantum coherence of $d-$dimensional quantum states based on $Cd_[m,M]$. The corresponding finite set of coherence witnesses is presented explicitly, which detects all the coherent states.
• Score: 0.07499722271664144
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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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