Coherence by measurement

Liangxue Fu, Fengli Yan, Ting Gao

Abstract We study block-coherence measures based on the resource theory of block-coherence and coherence measures based on positive-operator-valued measures (POVM). Several block-coherence measures are presented, including the block-coherence measure based on maximum relative entropy, the one-shot block-coherence cost under maximally block-incoherent operations, and the coherence measure based on coherent rank. Their relationships are obtained. Moreover, we describe the deterministic coherence dilution process by constructing block-incoherent operations. Based on the POVM coherence resource theory, we also propose two coherence measures and analyze their relationship.

Jan Peřina

C. L. Liu, Qi-Ming Ding, D. M. Tong

Abstract In this paper, we examine the superadditivity of convex roof coherence measures. We put forward a theorem on the superadditivity of convex roof coherence measures, which provides a sufficient condition to identify the convex roof coherence measures fulfilling the superadditivity. By applying the theorem to each of the known convex roof coherence measures, we prove that the coherence of formation and the coherence concurrence are superadditive, while the geometric measure of coherence, the convex roof coherence measure based on linear entropy, the convex roof coherence measure based on fidelity, and convex roof coherence measure based on -entropy are non-superadditive.

ALLAINE YA'SIN

Ho-Joon Kim, Soojoon Lee

Quantum dynamics governs the transformation of static quantum resources, such as coherence and entanglement, in both quantum states and measurements. Prior studies have established that a quantum channel's state-cohering power can be converted into the state-entangling power without additional coherence. Here, we complete this coherence-to-entanglement paradigm by demonstrating that a channel's measurement-cohering power can likewise be converted into the measurement-entangling power. This result reinforces, on the dynamical level, the intuition that entanglement emerges as a manifestation of coherence. To formalize this picture, we develop resource theories for measurement-cohering and measurement-entangling powers and characterize the structure of incoherent measurements to analyze measurement-coherence generation. Furthermore, we show that the state-cohering power of a quantum channel is equivalent to the measurement-cohering power of its adjoint map, and a corresponding equivalence also exists between the state-entangling power and the measurement-entangling power.