Symmetry of large physical systems implies independence of subsystems
Symmetry of large physical systems implies independence of subsystems
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DOI：
10.1038/nphys684
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发表时间：
2007-03
期刊：
影响因子：
19.6
通讯作者：
R. Renner
中科院分区：
文献类型：
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作者：
R. Renner
由大量相似子系统组成的复合系统在物理学和信息论的许多领域发挥着重要作用。然而，他们的分析通常依赖于子系统相互独立（或仅弱相关）的假设。在这里，我们证明了这一假设通常适用于对称的量子系统，即子系统排列下的不变性。由于对称性通常隐含在自然属性中，例如，相同粒子的不可区分性，因此其结果具有广泛的后果。特别是，它意味着可以通过应用于有限数量的（随机选择的）样本子系统的测量来估计大型复合系统的整体特性，这一事实对实验数据的解释很重要。此外，它推广了量子信息理论和密码学中的陈述，这些陈述以前只被认为在某些独立性假设下成立。
Composite systems consisting of a large number of similar subsystems play an important role in many areas of physics as well as in information theory. Their analysis, however, often relies on the assumption that the subsystems are mutually independent (or only weakly correlated). Here, we show that this assumption is generally justified for quantum systems that are symmetric, that is, invariant under permutations of the subsystems. Because symmetry is often implied by natural properties, for example, the indistinguishability of identical particles, the result has a wide range of consequences. In particular, it implies that global properties of a large composite system can be estimated by measurements applied to a limited number of (randomly chosen) sample subsystems, a fact that is important for the interpretation of experimental data. Moreover, it generalizes statements in quantum information theory and cryptography, which previously have only been known to hold under certain independence assumptions.