Given a non-empty closed convex subset F of density matrices, we formulate conditions that guarantee the existence of an F-morphism (namely, a completely positive trace-preserving linear map that maps F into itself) between two arbitrarily chosen density matrices. While we allow errors in the transition, the corresponding map is required to be an exact F-morphism. Our findings, though purely geometrical, are formulated in a resource-theoretic language and provide a common framework that comprises various resource theories, including the resource theories of bipartite and multipartite entanglement, coherence, athermality, and asymmetric distinguishability. We show how, when specialized to some situations of physical interest, our general results are able to unify and extend previous analyses. We also study conditions for the existence of maximally resourceful states, defined here as density matrices from which any other one can be obtained by means of a suitable F-morphism. Moreo...

中文翻译：

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具有精确资源形态的一般状态转换：统一的资源理论方法

给定密度矩阵的非空闭合凸子集F，我们制定了条件，保证在两个任意选择的密度矩阵之间存在F态（即，将F映射到其本身的完全正的保留迹线的线性图）。尽管我们允许转换中出现错误，但要求对应的图是精确的F晶态。我们的发现，尽管纯粹是几何的，但是以资源理论的语言表达的，并提供了一个包含各种资源理论的通用框架，其中包括两方和多方纠缠的资源理论，相干性，无热性和不对称的可区分性。我们将展示在专门针对某些身体感兴趣的情况时，我们的总体结果如何能够统一和扩展先前的分析。我们还研究了最大资源状态的存在条件，此处定义为密度矩阵，可以通过合适的F态从中获得任何其他状态。莫罗...