Intrinsic randomness as a measure of quantum coherence

By Xiao Yuan, Hongyi Zhou, Zhu Cao, Xiongfeng Ma. 2015

352 citations recorded by the source corpus.

Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a specific (classical) computational basis. Recently, by regarding coherence as a physical resource, Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] presented a comprehensive framework for coherence measures. Here, we propose a quantum coherence measure essentially using the intrinsic randomness of measurement. The proposed coherence measure provides an answer to the open question in completing the resource theory of coherence. Meanwhile, we show that the coherence distillation process can be treated as quantum extraction, which can be regarded as an equivalent process of classical random number extraction. From this viewpoint, the proposed coherence measure also clarifies the operational aspect of quantum coherence. Finally, our results indicate a strong similarity between two types of quantumness\char22{}coherence and entanglement.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/51567a3d8040eae8b971109058610aa25266dae3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Xiongfeng Ma
2. Hoi-Kwong Lo
3. Jian-Wei Pan
4. Feihu Xu
5. Qiang Zhang
6. Bing Qi
7. Vlatko Vedral
8. Yu-Ran Zhang

In Atomic and Molecular Physics, and Optics

1. Xiongfeng Ma
2. Hoi-Kwong Lo
3. Jian-Wei Pan
4. Feihu Xu
5. Qiang Zhang
6. Bing Qi
7. Vlatko Vedral
8. Heng Fan

Citations in the corpus

• Operational Resource Theory of Coherence. (2015, background): “We then show that in the asymptotic limit of many copies of a state, both are given by simple singleletter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence…”
• Quantum random number generation (2015, methodology): “In turn, quantum coherence can be quantified from intrinsic randomness.(14) A practical QRNG can be developed using the simple process as shown in Figure 1.”
• Operational one-to-one mapping between coherence and entanglement measures (2017, background): “When f (p) = −∑j pj log2 pj denotes the Shannon entropy, Ef is the celebrated entanglement of formation EF (coinciding with the relative entropy of entanglement Er for pure states) [1], and Cf is the coherence of formation CF [3,31] (equal to the coherence cost CC [28]).”
• Quantum coherence and geometric quantum discord (2017, background): “Based on this consideration, Yuan et al. (2015) proposed a 24 convex roof measure for coherence, which has been proved to satisfy the four conditions of Baumgratz et al. (2014).”
• Secure quantum key distribution with realistic devices (2020, background): “Interestingly, this unpredictability on the (computational) Z-basis is quantified by the coherence measure in the resource theory (Yuan et al., 2015), which is recently connected to the security of QKD (Ma et al., 2019).”