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Quantitative analysis of inherent quantum properties using quantum resource theories reveals fundamental limitations and advantages of large-scale quantum information processing in various tasks. However, a conventional way of resource quantification by resource measures may contradict rates of asymptotic transformation between resourceful quantum states on a large scale due to an approximation in the transformation. In this paper, we investigate consistent resource measures, which quantify resources without contradicting the rates of the asymptotic resource transformation. We prove that relative entropic measures are consistent with the rates for a broad class of resources, i.e., all convex finite-dimensional resources, e.g., entanglement, coherence, and magic, and even some non-convex or infinite-dimensional resources such as quantum discord, non-Markovianity, and non-Gaussianity. These results show that consistent resource measures are widely applicable to the quantitative analysis of large-scale quantum information processing using various quantum resources.Quantum resource theories (QRTs) [1, 2] provide a unified framework for quantitatively analyzing quantum properties, which underlies the advantage of quantum information processing over classical information processing. The framework of QRTs was initially motivated by the entanglement theory [3], but similar formulations apply to enormous kinds of quantum properties such as coherence [4], magic states [5, 6, 7], discord [8], non-Markovianity [9, 10], non-Gaussianity [11, 12, 13, 14]. Recently, general frameworks to reveal the universal properties of these various resources have also been studied [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2].Quantification of resources, along with manipulation, is one of the major interests of QRTs [26, 27, 28, 29, 30, 31, 32]. To quantify resources, we use real-valued functions of states called resource measures. Resource measures can quantify resources without contradicting convertibility of resources; that is, the resource amount quantified by a resource measure does not increase when we transform a resource by free operations exactly, i.e., without error. For example, the relative entropic measure, that is, the relative entropy between a given state and the closest free state to the given state, is conventionally used in various QRTs [33, 5, 34, 35, 36, 37, 38]. On the other hand, it is known that resources are not necessarily comparable in terms of the exact convertibility. For example, in the QRT of magic for qutrits, there are two classes of states (the Strange states and the Norrell states) impossible to be exactly converted to each other using free operations [5]. Moreover, considering large-scale quantum information processing, where the fundamental advantages of quantum resources evidently emerge compared with one-shot cases, we also need to investigate asymptotic state conversion, where many copies of a given state are converted by free operations into many copies of a target state within a vanishingly small but nonzero error. Therefore, it is vital to investigate properties of resource measures associated also without contradicting the asymptotic state conversion (in addition to the exact conversion). While these two concepts, resource measures and asymptotic state conversion, are previously discussed separately, a concept of consistency of resource measures was introduced in Ref. [2], which associates the quantification of resources with the asymptotic state conversion. A consistent resource measure is defined to quantify resources without contradicting the rates of the asymptotic state conversion as well as the exact conversion. Reference [2] also shows that the relative entropic measure serves as a consistent resource measure in QRTs with particular restrictions, namely, convex and finite-dimensional QRTs with a full-rank free state.However, physically well-motivated resources do not necessarily satisfy these restrictions. For example, the sets of states that have no quantum discord, e.g., classical-classical states and classical-quantum states, are not convex.[8]. In addition, the set of quantum Markov chains [39] and that of Gaussian states [40] are also known to be non-convex. Moreover, the Gaussian states are defined on an infinite-dimensional state space. Therefore, when we regard these properties as quantum resources, the existing technique for proving the consistency of the entropic measure is no longer directly applicable. At the same time, it is still not evident whether the relative entropic measure is also consistent in such non-convex or infinite-dimensional QRTs.In this paper, we investigate the relative entropic measure as a prospective candidate of a consistent resource measure even for more general classes of resources than the previous research [2]. First, by improving the definition of consistent resource measures, we show that the relative entropic measure becomes consistent in all finite-dimensional convex QRTs even without full-rank free states. Next, as examples of non-convex but physically well-motivated resources, we study discord and non-Markovianity. Even though the proof technique of the previous work is not directly applicable due to the non-convexity, we show that the relative entropic measure is consistent also for these resources. Finally, as an example of resources emerging on an infinite-dimensional state space, we consider non-Gaussianity. Despite the previous literature claiming the continuity of the relative entropic measure [38], we show a counterexample to the continuity even under reasonable energy constraints. Then, we consider a convex QRT of non-Gaussianity [11, 12] and prove that the relative entropic measure in this convex formulation is asymptotically continuous and consistent if the energy of a given system is appropriately constrained.Our results show the existence of a consistent resource measure even for general resources including discord, non-Markovianity, and non-Gaussianity, which are not covered in the previous work on consistent resource measures. Thus, we shed new light on the quantification of non-convex and infinite-dimensional resources from the perspective of the consistency of resource measures motivated by large-scale quantum information processing. We believe that our investigation for consistent resource measures leads to further understandings of quantifications of resources useful for studying large-scale quantum information processing and a larger class of physically well-motivated quantum phenomena.II Consistent resource measureIn this section, we provide a brief review of consistent resource measures. (For more details, see Sections 6.3 and 6.4 of [2].) Throughout this paper, we let