资源的全序化：量子-经典分离
Total Ordering of Resources: A Quantum-Classical Separation
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中文总结 AI 辅助
该研究证明维度大于2的量子系统无法实现资源的全序化，而经典系统可以，从而揭示了量子与经典态转化之间的根本性差异。
中文摘要 AI 辅助
量子信息科学的一个核心目标是理解哪些物理态可以转化为其他态。理想的情形是一个全序系统，其中每个态都可以用一个单一的值进行排序，并且排序较高的态总是可以转化为排序较低的态。这样的排序将提供态可转化性的完整描述，使资源结构在表征和比较上达到最大程度的简化。我们证明，对于任何维度大于2的量子系统，这种简单的排序在根本上是不可行的。量子力学的基本性质保证了某些态总是不可比较的。此外，我们通过构造任意大小的经典系统来表明这是一个独特的量子现象，这些经典系统可以被完美地排序。这建立了量子与经典态转化之间一个严格且引人注目的分界。
英文摘要
A central goal in quantum information science is understanding which physical states can be converted into others. The ideal scenario would be a totally ordered system, where every state can be ranked by a single value, and a higher-ranked state can always be converted into a lower-ranked one. Such an ordering would provide a complete description of state convertibility, making the resource structure maximally simple to characterize and compare. We prove that such a simple ordering is fundamentally impossible for any quantum system with dimension larger than 2. The underlying properties of quantum mechanics guarantee that some states will always be incomparable. Furthermore, we show this is a uniquely quantum phenomenon by constructing classical systems of any size that can be perfectly ranked. This establishes a rigorous and striking divide between quantum and classical state transformations.
发表机构
- Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所在）
- Departamento de Matemáticas, Universidad Carlos III de Madrid（马德里卡洛斯三世大学数学系）
- Instituto de Ciencias Matemáticas (ICMAT)（马德里高等数学研究所）
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