title: Directly Measuring the Degree of Quantum Coherence using Interference Fringes.
abstract: Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Yi-Tao
authors.initials: YT
authors.lastname: Wang
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Jian-Shun
authors.initials: JS
authors.lastname: Tang
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Zhi-Yuan
authors.initials: ZY
authors.lastname: Wei
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Shang
authors.initials: S
authors.lastname: Yu
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Zhi-Jin
authors.initials: ZJ
authors.lastname: Ke
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Xiao-Ye
authors.initials: XY
authors.lastname: Xu
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Chuan-Feng
authors.initials: CF
authors.lastname: Li
authors.affiliation: CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Guang-Can
authors.initials: GC
authors.lastname: Guo