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arXiv quant-ph/0701051quant-ph
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连续变量系统的正则和微正则典型纠缠

Canonical and micro-canonical typical entanglement of continuous variable systems

A. Serafini, O. C. O. Dahlsten, D. Gross, M. B. Plenio

摘要:

我们提出了一个框架,符合统计力学的一般规范原则,定义连续变量系统的纯高斯态集上的措施。在这样一个框架内,我们定义了两个具体的措施,被称为“微正则”和“正则”,并应用它们来系统地研究的统计特性的二分纠缠的n模纯高斯态(量化的熵的子系统)。我们严格证明了“浓度的措施”周围的一个有限的平均值,发生在规范和微规范的方法在量子极限的纠缠。对于有限的n,我们确定分析的平均值和标准偏差的纠缠(量化的减少纯度)之间的一个模式和所有其他模式。此外,我们数值研究更一般的情况下,清楚地表明,开始的浓度的措施已经发生在相对较小的n。

英文摘要:

We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as `micro-canonical' and `canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n-mode pure Gaussian states (as quantified by the entropy of a subsystem). We rigorously prove the "concentration of measure" around a finite average, occurring for the entanglement in the thermodynamical limit in both the canonical and the micro-canonical approach. For finite n, we determine analytically the average and standard deviation of the entanglement (as quantified by the reduced purity) between one mode and all the other modes. Furthermore, we numerically investigate more general situations, clearly showing that the onset of the concentration of measure already occurs at relatively small n.

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