Operational axioms for diagonalizing states
Operational axioms for diagonalizing states
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对角化状态的运算公理
DOI：
10.4204/eptcs.195.8
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发表时间：
2015
期刊：
影响因子：
1.8
通讯作者：
Carlo Maria Scandolo
中科院分区：
文献类型：
--
作者：
G. Chiribella;Carlo Maria Scandolo
在量子理论中，每个状态都可以对角化，即分解为完全可区分的纯状态的凸组合。这种基本结构在量子力学、量子信息论和量子统计力学中起着无处不在的作用，它为多数化和熵的概念提供了基础。一个自然的问题出现了：我们能从纯粹的操作公理中重建这些概念吗？我们在一般概率论的框架中解决了这个问题，提出了一组公理，保证每个状态都可以对角化。第一个公理是因果性，它保证了二部态的边缘被很好地定义。然后，纯度保持声明纯变换集合在复合下是封闭的。第三个公理是净化，它允许为系统与其环境的组合分配一个纯净状态。最后，我们引入了纯锐性公理，说明对于每一个系统，在某个状态上至少存在一个以单位概率发生的纯效应。对于满足这四个公理的理论，我们给出了对角化每个给定状态的构造算法。对角化结果使我们能够在纯操作资源理论中形成捕获状态可转换性的多数化准则，其中随机可逆转换被视为自由操作。
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations.
量子数学物理
DOI：
10.1007/978-3-319-26902-3
发表时间：
2016
期刊：
影响因子：
--
作者：
Finster;J. Kleiner;C. Röken;J. Tolksdorf
通讯作者：
J. Tolksdorf
影响因子：
--
作者：
Barnum H
通讯作者：
Barnum H