Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.arXiv:1812.09216v2 [quant-ph]

We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operationindependent equality rather than operation-dependent inequalities and therefore applicable to various physical contexts. Our framework is compatible with all the known results on coherence measures but much more flexible and convenient for applications, and by using it many open questions can be resolved.Quantum coherence is a fundamental feature of quantum mechanics, describing the capability of a quantum state to exhibit quantum interference phenomena. It is an essential ingredient in quantum information processing [1], and plays a central role in emergent fields, such as quantum metrology [2][3][4], nanoscale thermodynamics [5][6][7][8][9][10][11], and quantum biology [12][13][14][15][16]. Although the theory of quantum coherence is historically well developed in quantum optics [17][18][19], it is only in recent years that the quantification of coherence has attracted a growing interest [20][21][22][23][24] due to the development of quantum information science.By following the approach that has been established for entanglement resource [25,26], Baumgratz et al. proposed a seminal framework for quantifying coherence as a resource in Ref. [22]. The framework comprises four conditions, of which the first two are based on the notions of free states and free operations in the resource theories, while the third and fourth conditions are two constraints imposed on coherence measures. Based on this framework, a number of coherence measures, such as the relative entropy of coherence, the l 1 norm of coherence, and the coherence of formation [20,22,27,28], have been put forward. With the coherence measures, various properties of quantum coherence, such as the relations between quantum coherence and quantum correlations [29][30][31][32][33], the freezing phenomenon of coherence [34,35], and the distillation of coherence [28,36], were investigated. Hereafter, we refer to the framework proposed by Baumgratz et al. as the BCP framework for simplicity.Although the BCP framework has been widely used as an approach to coherence measures, there are arguments against the necessity of its last two conditions [29,37], and researchers have different opinions on the definition of free operations. Besides the incoherent operations defined in the BCP framework, there have been many different suggestions on the definition of free operations, such as maximally incoherent operations [20], translationally invariant operations [23], and others [38][39][40]. These arguments against the conditions and free operations imply that the frameworks for quantifying coherence are not unique. There can be other frameworks different from the BCP framework. For instance, the framework proposed by Marvian and Spekkens in Ref. [23], called the MS framework for simplicity, is based on the translationally invariant operations, and it compris...

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.