Classifying coherence with a finite set of witnesses

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 $C_{[m,M]}^d$. We present necessary and sufficient conditions of detecting quantum coherence of $d-$dimensional quantum states based on $C_{[m,M]}^d$. 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.

7 pages,2 figures

References in corpus (17)

• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Observable measure of quantum coherence in finite dimensional systems
• Role of quantum coherence in chromophoric energy transport
• Witnessing Quantum Coherence: from solid-state to biological systems
• Necessary and sufficient conditions for bipartite entanglement
• Detecting and estimating coherence based on coherence witnesses
• When different entanglement witnesses detect entangled states simultaneously
• Quantitative Coherence Witness for Finite Dimensional States
• Maximum Relative Entropy of Coherence for Quantum Channels
• Signatures of superradiance as a witness to multipartite entanglement
• Tomographic Witnessing and Holographic Quantifying of Coherence
• Common Coherence Witnesses and Common Coherent States
• Accessing continuous-variable entanglement witnesses with multimode spin observables
• Bloch vectors for qudits and geometry of entanglement
• Witnessing quantum coherence with prior knowledge of observables
• Interrelation of nonclassicality conditions through stabiliser group homomorphism