Quantum Coherence and Intrinsic Randomness. Issue 11 (27th August 2019) - Yuan, Xiao; Zhao, Qi; Girolami, Davide; Ma, Xiongfeng
Abstract: The peculiar uncertainty or randomness of quantum measurements stems from quantum coherence, whose information‐theoretic characterization is currently under investigation. The resource theory of coherence investigates interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as a resource for generating intrinsic randomness by measuring a state in the computational basis. It is observed in a previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a correlated party (classical system) about the system measurement outcome. In this work, the result is re‐derived from a quantum point of view, and then the intrinsic randomness is connected to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there do not exist bound coherent states, these two coherence measures—intrinsic randomness quantified by coherence of formation and by relative entropy of coherence—are different. Interestingly, it is shown that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system. Abstract : Coherence is a resource to quantify the unpredictable intrinsic randomness existing in the measurement outcomes of the computational basis. Here, the operational interpretations of the relative entropy of coherence and the coherence of formation in characterizing intrinsic randomness are established. The gap of the two coherence measures is equal to the quantum discord.